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Title: Minimisers in the core threshold formula of random $k$-uniform hypergraphs-Definition: For integers $k\geq2$ and $r\geq2$, other than $(k,r)=(2,2)$, $\lambda_{k,r}$- is the positive $\lambda$ that minimises $\lambda/(kQ(\lambda,r-1)^{k-1})$, where- $Q(\lambda,s)=\mathbb{P}(\mathrm{Po}(\lambda)\geq s)$. This minimum gives the $r$-core- threshold $c_{k,r}$ of a random $k$-uniform hypergraph CITE{WikiHypergraph}; when- $k=2$, it is half the usual average-degree threshold of a random graph.+Definition: For integers $k\geq2$ and $r\geq2$, except $(2,2)$, $\lambda_{k,r}$ is+ the positive $\lambda$ that minimises $\lambda/(kQ(\lambda,r-1)^{k-1})$; here $Q(\lambda,s)=\mathbb{P}(\mathrm{Po}(\lambda)\geq+ s)$. The formula is for random $k$-uniform hypergraphs CITE{WikiHypergraph}. Keywords: random hypergraph core, Poisson parameter, core threshold minimiser Parameters:
number-header: $\lambda_{k,r}$ Numbers:-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,2}[$c_{3,2}$].- params:- k: '3'- r: '2'- number: '1.256431208626169676982737616609216326916416831701323711125894727048300478541051903533664750947250849'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,3}[$c_{3,3}$].- params:- k: '3'- r: '3'- number: '3.213563520216979243990721598628550332961016937266993935011570314990932508944562066900919080501639543'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,4}[$c_{3,4}$].- params:- k: '3'- r: '4'- number: '4.921981846772290888776752883024317186056436573439824091508273468468509196715986475449901324256178986'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,5}[$c_{3,5}$].- params:- k: '3'- r: '5'- number: '6.515591826097798170851877858293313883072308134824081056860046654688644744395191367617398426422648410'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,6}[$c_{3,6}$].- params:- k: '3'- r: '6'- number: '8.039263820146856092138856254339199422167993794012407995996779695584362939354934009423133546902118161'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,7}[$c_{3,7}$].- params:- k: '3'- r: '7'- number: '9.514469508880899030507393558450993274264377875660089436754383763320216720140867547689851121592635562'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,8}[$c_{3,8}$].- params:- k: '3'- r: '8'- number: '10.95346075985564844256143919627797293749795469545187124088935549568731785512016948741082119567842981'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,2}[$c_{4,2}$].- params:- k: '4'- r: '2'- number: '1.903813694440383484710140360828135127280364804561987445879389818281945875445251742935897221209070264'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,3}[$c_{4,3}$].- params:- k: '4'- r: '3'- number: '3.943432991608201993709553168630446799608703563709097909739285068630870979892017973839711377125004985'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,4}[$c_{4,4}$].- params:- k: '4'- r: '4'- number: '5.712655689793184261749113193644386168167982023993296659606920984267937821370298005601033912014038776'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,5}[$c_{4,5}$].- params:- k: '4'- r: '5'- number: '7.356238662572010428146260839034522811851758906746380894035040209606244738087812519651127293227178069'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,6}[$c_{4,6}$].- params:- k: '4'- r: '6'- number: '8.923133543937897404138547779823342524209920334968527807245157335182798107944509307833635497158032921'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,7}[$c_{4,7}$].- params:- k: '4'- r: '7'- number: '10.43685728939695192283051786477345424635359010958106227104559457532044084712440111362795839930312800'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,8}[$c_{4,8}$].- params:- k: '4'- r: '8'- number: '11.91085482297029987283273947363803164895241207451413619648971821871543101470988522101009737414578049'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,2}[$c_{5,2}$].- params:- k: '5'- r: '2'- number: '2.336662982263053881182850266714011154679504739557109039685225120116767568104385781543593285556392922'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,3}[$c_{5,3}$].- params:- k: '5'- r: '3'- number: '4.429961741174340595794299265887946343440849798841691898549878810448210800725524242240549510592604875'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,4}[$c_{5,4}$].- params:- k: '5'- r: '4'- number: '6.239233099841364699091761779242710268467766957008527239152171992449855251908655717861069860689669939'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,5}[$c_{5,5}$].- params:- k: '5'- r: '5'- number: '7.915932808932573244389888265459534420745939469008615284488694955445411352543868387413870342466396931'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,6}[$c_{5,6}$].- params:- k: '5'- r: '6'- number: '9.511581543348483155284054757333259972267475267373966015269183105044286077661111762509825055266705227'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,7}[$c_{5,7}$].- params:- k: '5'- r: '7'- number: '11.05099850311515789634766292263302508532769550742277390402251011897664690455990175411305835670362303'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,8}[$c_{5,8}$].- params:- k: '5'- r: '8'- number: '12.54839414688261437023640741484170199310321861483385964228059641879490595267312347778684332551874187'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,2}[$c_{6,2}$].- params:- k: '6'- r: '2'- number: '2.660399058463684990432673112693838761316192793557399779133621108141380344526679670369701126317582048'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,3}[$c_{6,3}$].- params:- k: '6'- r: '3'- number: '4.792922350729458389393836269395977881768808104455610404765378350938009353293442180198297113646891715'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,4}[$c_{6,4}$].- params:- k: '6'- r: '4'- number: '6.631692044980859859695457087456113562828943559209647679904601932328360504449403525078647056405154631'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,5}[$c_{6,5}$].- params:- k: '6'- r: '5'- number: '8.332885060545474643453038367357276844362292641194579907242869038284539339311870952451145000236630570'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,6}[$c_{6,6}$].- params:- k: '6'- r: '6'- number: '9.949856035279598965993281101298144352595406559863380482666470886487477439749560118793565830379607461'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,7}[$c_{6,7}$].- params:- k: '6'- r: '7'- number: '11.50836092309161955292977618826790777947661320182321955172192652659584731470204336130700207829174634'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,8}[$c_{6,8}$].- params:- k: '6'- r: '8'- number: '13.02316374017669072156336769629112584326498148263216486482457051849391131216069892990076318148638379'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,2}[$c_{7,2}$].- params:- k: '7'- r: '2'- number: '2.918300475783052591304221719797499459970061873861584609944495208244877889764383735414949103879265396'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,3}[$c_{7,3}$].- params:- k: '7'- r: '3'- number: '5.081459160901541280072984052767384364834705608549266804400302362457469786927329892961576241670256255'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,4}[$c_{7,4}$].- params:- k: '7'- r: '4'- number: '6.943403149510170669582130838854226834674871175506322769216454740852507523491016500409957336861346672'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,5}[$c_{7,5}$].- params:- k: '7'- r: '5'- number: '8.663897435137174519899583577567728252667605281255596605005591025135471805928532424709794084516994332'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,6}[$c_{7,6}$].- params:- k: '7'- r: '6'- number: '10.29770370948003437532796512255737443462847796934890923922314195797931097072888681130447394638516963'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,7}[$c_{7,7}$].- params:- k: '7'- r: '7'- number: '11.87130070214323957227718493587230991764172191009718801979638624429793118363290687748586153232250824'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,8}[$c_{7,8}$].- params:- k: '7'- r: '8'- number: '13.39988120401632761753924670661057126272293378422422449028809204749315606537864394912727852237790303'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,2}[$c_{8,2}$].- params:- k: '8'- r: '2'- number: '3.132265450540420106833422460869303332477500804253648991520139627783433414358227583586491785309904738'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,3}[$c_{8,3}$].- params:- k: '8'- r: '3'- number: '5.320410398592856390274399571423194057429031818068357224721914044015662800282969722273689295179037782'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,4}[$c_{8,4}$].- params:- k: '8'- r: '4'- number: '7.201342167086465465995230954511332137013680863221225905126416091272120474693659568328505902778556493'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,5}[$c_{8,5}$].- params:- k: '8'- r: '5'- number: '8.937689058821257897847473075778498054363562033589717691202034236556493355565920677841425777848131716'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,6}[$c_{8,6}$].- params:- k: '8'- r: '6'- number: '10.58534398664845734750878149290269445326079627643095634678228319037799585247784783513560945584997527'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,7}[$c_{8,7}$].- params:- k: '8'- r: '7'- number: '12.17136936664993198917735237904287147986248521678215131664326659268714127192768870112217956585325223'-- comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,8}[$c_{8,8}$].- params:- k: '8'- r: '8'- number: '13.71130531896385558662755379683587375766125942222105380706720345280147382907814364034891657375807970'-- params:- k: '2'- r: '3'- number: '1.793282132900761007557553363901042400798495011352844840187368692793640350312145307101816031284552000'- comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#3}[$c_3$],- in average-degree normalisation.-- params:- k: '2'- r: '4'- number: '3.383634282853181326233720626325268824492707241179045519190265623070215823455522487634872897545945707'- comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#4}[$c_4$],- in average-degree normalisation.-- params:- k: '2'- r: '5'- number: '4.881277491345664699476221132699578165991747552538638780470402006490011336193449645628928782932652016'- comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#5}[$c_5$],- in average-degree normalisation.-- params:- k: '2'- r: '6'- number: '6.322505551033348213117536010712698139853551563542760107474509790804292377580695833711266516282831955'- comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#6}[$c_6$],- in average-degree normalisation.-- params:- k: '2'- r: '7'- number: '7.724583600437083719742881506618773234074923503267538261336546494114206039730648969106716340789423916'- comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#7}[$c_7$],- in average-degree normalisation.-- params:- k: '2'- r: '8'- number: '9.097344402575752511530172721804952369723320459976861539455985671621454422104751816436773258597298092'- comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#8}[$c_8$],- in average-degree normalisation.-- params:- k: '2'- r: '9'- number: '10.44703068132582643466146774023156489999628189515940834443242756856517508061830202668735584626248927'- comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#9}[$c_9$],- in average-degree normalisation.-- params:- k: '2'- r: '10'- number: '11.77790660645444814760342031501205362589525223509565135072961175420145126514944898686789068160617415'- comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#10}[$c_10$],- in average-degree normalisation.-- params:- k: '2'- r: '11'- number: '13.09304249828627741818047196896153062418531383505357205182742728349180778379297745359746436233268261'- comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#11}[$c_11$],- in average-degree normalisation.-- params:- k: '2'- r: '12'- number: '14.39473890191730692303041347143866646079914037894170847648844652786607945528956529938703860316494576'- comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#12}[$c_12$],- in average-degree normalisation.+ '3':+ '2':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,2}[$c_{3,2}$].+ number: '1.256431208626169676982737616609216326916416831701323711125894727048300478541051903533664750947250849'+ '3':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,3}[$c_{3,3}$].+ number: '3.213563520216979243990721598628550332961016937266993935011570314990932508944562066900919080501639543'+ '4':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,4}[$c_{3,4}$].+ number: '4.921981846772290888776752883024317186056436573439824091508273468468509196715986475449901324256178986'+ '5':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,5}[$c_{3,5}$].+ number: '6.515591826097798170851877858293313883072308134824081056860046654688644744395191367617398426422648410'+ '6':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,6}[$c_{3,6}$].+ number: '8.039263820146856092138856254339199422167993794012407995996779695584362939354934009423133546902118161'+ '7':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,7}[$c_{3,7}$].+ number: '9.514469508880899030507393558450993274264377875660089436754383763320216720140867547689851121592635562'+ '8':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#3,8}[$c_{3,8}$].+ number: '10.95346075985564844256143919627797293749795469545187124088935549568731785512016948741082119567842981'+ '4':+ '2':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,2}[$c_{4,2}$].+ number: '1.903813694440383484710140360828135127280364804561987445879389818281945875445251742935897221209070264'+ '3':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,3}[$c_{4,3}$].+ number: '3.943432991608201993709553168630446799608703563709097909739285068630870979892017973839711377125004985'+ '4':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,4}[$c_{4,4}$].+ number: '5.712655689793184261749113193644386168167982023993296659606920984267937821370298005601033912014038776'+ '5':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,5}[$c_{4,5}$].+ number: '7.356238662572010428146260839034522811851758906746380894035040209606244738087812519651127293227178069'+ '6':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,6}[$c_{4,6}$].+ number: '8.923133543937897404138547779823342524209920334968527807245157335182798107944509307833635497158032921'+ '7':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,7}[$c_{4,7}$].+ number: '10.43685728939695192283051786477345424635359010958106227104559457532044084712440111362795839930312800'+ '8':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#4,8}[$c_{4,8}$].+ number: '11.91085482297029987283273947363803164895241207451413619648971821871543101470988522101009737414578049'+ '5':+ '2':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,2}[$c_{5,2}$].+ number: '2.336662982263053881182850266714011154679504739557109039685225120116767568104385781543593285556392922'+ '3':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,3}[$c_{5,3}$].+ number: '4.429961741174340595794299265887946343440849798841691898549878810448210800725524242240549510592604875'+ '4':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,4}[$c_{5,4}$].+ number: '6.239233099841364699091761779242710268467766957008527239152171992449855251908655717861069860689669939'+ '5':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,5}[$c_{5,5}$].+ number: '7.915932808932573244389888265459534420745939469008615284488694955445411352543868387413870342466396931'+ '6':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,6}[$c_{5,6}$].+ number: '9.511581543348483155284054757333259972267475267373966015269183105044286077661111762509825055266705227'+ '7':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,7}[$c_{5,7}$].+ number: '11.05099850311515789634766292263302508532769550742277390402251011897664690455990175411305835670362303'+ '8':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#5,8}[$c_{5,8}$].+ number: '12.54839414688261437023640741484170199310321861483385964228059641879490595267312347778684332551874187'+ '6':+ '2':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,2}[$c_{6,2}$].+ number: '2.660399058463684990432673112693838761316192793557399779133621108141380344526679670369701126317582048'+ '3':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,3}[$c_{6,3}$].+ number: '4.792922350729458389393836269395977881768808104455610404765378350938009353293442180198297113646891715'+ '4':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,4}[$c_{6,4}$].+ number: '6.631692044980859859695457087456113562828943559209647679904601932328360504449403525078647056405154631'+ '5':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,5}[$c_{6,5}$].+ number: '8.332885060545474643453038367357276844362292641194579907242869038284539339311870952451145000236630570'+ '6':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,6}[$c_{6,6}$].+ number: '9.949856035279598965993281101298144352595406559863380482666470886487477439749560118793565830379607461'+ '7':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,7}[$c_{6,7}$].+ number: '11.50836092309161955292977618826790777947661320182321955172192652659584731470204336130700207829174634'+ '8':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#6,8}[$c_{6,8}$].+ number: '13.02316374017669072156336769629112584326498148263216486482457051849391131216069892990076318148638379'+ '7':+ '2':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,2}[$c_{7,2}$].+ number: '2.918300475783052591304221719797499459970061873861584609944495208244877889764383735414949103879265396'+ '3':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,3}[$c_{7,3}$].+ number: '5.081459160901541280072984052767384364834705608549266804400302362457469786927329892961576241670256255'+ '4':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,4}[$c_{7,4}$].+ number: '6.943403149510170669582130838854226834674871175506322769216454740852507523491016500409957336861346672'+ '5':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,5}[$c_{7,5}$].+ number: '8.663897435137174519899583577567728252667605281255596605005591025135471805928532424709794084516994332'+ '6':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,6}[$c_{7,6}$].+ number: '10.29770370948003437532796512255737443462847796934890923922314195797931097072888681130447394638516963'+ '7':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,7}[$c_{7,7}$].+ number: '11.87130070214323957227718493587230991764172191009718801979638624429793118363290687748586153232250824'+ '8':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#7,8}[$c_{7,8}$].+ number: '13.39988120401632761753924670661057126272293378422422449028809204749315606537864394912727852237790303'+ '8':+ '2':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,2}[$c_{8,2}$].+ number: '3.132265450540420106833422460869303332477500804253648991520139627783433414358227583586491785309904738'+ '3':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,3}[$c_{8,3}$].+ number: '5.320410398592856390274399571423194057429031818068357224721914044015662800282969722273689295179037782'+ '4':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,4}[$c_{8,4}$].+ number: '7.201342167086465465995230954511332137013680863221225905126416091272120474693659568328505902778556493'+ '5':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,5}[$c_{8,5}$].+ number: '8.937689058821257897847473075778498054363562033589717691202034236556493355565920677841425777848131716'+ '6':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,6}[$c_{8,6}$].+ number: '10.58534398664845734750878149290269445326079627643095634678228319037799585247784783513560945584997527'+ '7':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,7}[$c_{8,7}$].+ number: '12.17136936664993198917735237904287147986248521678215131664326659268714127192768870112217956585325223'+ '8':+ comment: The associated core threshold is HREF{Core_thresholds_of_random_k-uniform_hypergraphs#8,8}[$c_{8,8}$].+ number: '13.71130531896385558662755379683587375766125942222105380706720345280147382907814364034891657375807970'+ '2':+ '3':+ number: '1.793282132900761007557553363901042400798495011352844840187368692793640350312145307101816031284552000'+ comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#3}[$c_3$],+ in average-degree normalisation.+ '4':+ number: '3.383634282853181326233720626325268824492707241179045519190265623070215823455522487634872897545945707'+ comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#4}[$c_4$],+ in average-degree normalisation.+ '5':+ number: '4.881277491345664699476221132699578165991747552538638780470402006490011336193449645628928782932652016'+ comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#5}[$c_5$],+ in average-degree normalisation.+ '6':+ number: '6.322505551033348213117536010712698139853551563542760107474509790804292377580695833711266516282831955'+ comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#6}[$c_6$],+ in average-degree normalisation.+ '7':+ number: '7.724583600437083719742881506618773234074923503267538261336546494114206039730648969106716340789423916'+ comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#7}[$c_7$],+ in average-degree normalisation.+ '8':+ number: '9.097344402575752511530172721804952369723320459976861539455985671621454422104751816436773258597298092'+ comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#8}[$c_8$],+ in average-degree normalisation.+ '9':+ number: '10.44703068132582643466146774023156489999628189515940834443242756856517508061830202668735584626248927'+ comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#9}[$c_9$],+ in average-degree normalisation.+ '10':+ number: '11.77790660645444814760342031501205362589525223509565135072961175420145126514944898686789068160617415'+ comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#10}[$c_10$],+ in average-degree normalisation.+ '11':+ number: '13.09304249828627741818047196896153062418531383505357205182742728349180778379297745359746436233268261'+ comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#11}[$c_11$],+ in average-degree normalisation.+ '12':+ number: '14.39473890191730692303041347143866646079914037894170847648844652786607945528956529938703860316494576'+ comment: The corresponding graph $r$-core threshold is HREF{k-core_thresholds_of_the_Erdős_Rényi_random_graph#12}[$c_12$],+ in average-degree normalisation.
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