History of Cuckoo hashing thresholds of random $k$-uniform hypergraphs

 Display properties:   number-header: $c^*_{k,\ell}$-Numbers: []+Numbers:+- params:+    k: '2'+    ell: '1'+  number: 1/2+  comment: 'The threshold is exact: with two choices and capacity one, success is+    equivalent to the cuckoo graph being a pseudoforest.'+- params:+    k: '2'+    ell: '2'+  number: '1.794023736482697185702072260922220651446847857242629314741409159722842192323768658125858982706009313'+  comment: The root is $\xi_{2,2}=2.68799934550$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $1.7940237365$ to ten decimal+    places, in their row $\ell=3$ CITE{DGMMPR}.+- params:+    k: '2'+    ell: '3'+  number: '2.877462805773104601383446482855977688201566330213884344147609954701014361992024001432142349800224667'+  comment: The root is $\xi_{2,3}=5.07146970816$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $2.8774628058$ to ten decimal+    places, in their row $\ell=4$ CITE{DGMMPR}.+- params:+    k: '2'+    ell: '4'+  number: '3.921479097144247218622967455754882381969492446973709771717838244012920761856240928180429377430730329'+  comment: The root is $\xi_{2,4}=7.32170335898$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $3.9214790971$ to ten decimal+    places, in their row $\ell=5$ CITE{DGMMPR}.+- params:+    k: '2'+    ell: '5'+  number: '4.947756809299554345341872647115200280183738143165187479042937229462595359361250598170477473285153512'+  comment: The root is $\xi_{2,5}=9.49611633963$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $4.9477568093$ to ten decimal+    places, in their row $\ell=6$ CITE{DGMMPR}.+- params:+    k: '2'+    ell: '6'+  number: '5.964436239513138659619929120753446763597136707162676068555810567304407986993679162958098898424796905'+  comment: The root is $\xi_{2,6}=11.6220108348$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $5.9644362395$ to ten decimal+    places, in their row $\ell=7$ CITE{DGMMPR}.+- params:+    k: '3'+    ell: '1'+  number: '0.9179352766580860135154412282330241295566462813786741119388567679432894341028061252100137350717952174'+  comment: The root is $\xi_{3,1}=2.14912579991$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $0.9179352767$ to ten decimal+    places, in their row $\ell=2$ CITE{DGMMPR}.+- params:+    k: '3'+    ell: '2'+  number: '1.976402827945018131920271559975262298624969301245582124244029051282683200685764557735583055769410083'+  comment: The root is $\xi_{3,2}=5.65657634943$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $1.9764028279$ to ten decimal+    places, in their row $\ell=3$ CITE{DGMMPR}.+- params:+    k: '3'+    ell: '3'+  number: '2.991857217756977366680597685191668449623460870257231553720467580809494674831252223618984007293033939'+  comment: The root is $\xi_{3,3}=8.84985165247$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $2.9918572178$ to ten decimal+    places, in their row $\ell=4$ CITE{DGMMPR}.+- params:+    k: '3'+    ell: '4'+  number: '3.997012625648743302273762929913638565700653571578426870112509258493357375813089713288050426564473161'+  comment: The root is $\xi_{3,4}=11.9332406302$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $3.9970126256$ to ten decimal+    places, in their row $\ell=5$ CITE{DGMMPR}.+- params:+    k: '3'+    ell: '5'+  number: '4.998873294118150969333519117221896576217294921858737152365000264583014045776775919936019685113750641'+  comment: The root is $\xi_{3,5}=14.9703579883$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $4.9988732941$ to ten decimal+    places, in their row $\ell=6$ CITE{DGMMPR}.+- params:+    k: '3'+    ell: '6'+  number: '5.999568880504426099670108020028966633364065673199424477936168744197318069564183158242503476062116963'+  comment: The root is $\xi_{3,6}=17.9869322967$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $5.9995688805$ to ten decimal+    places, in their row $\ell=7$ CITE{DGMMPR}.+- params:+    k: '4'+    ell: '1'+  number: '0.9767701648780461315596453315801681767089324117092366344477820171954417168938976107089484319269740715'+  comment: The root is $\xi_{4,1}=3.59351196945$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $0.9767701649$ to ten decimal+    places, in their row $\ell=2$ CITE{DGMMPR}.+- params:+    k: '4'+    ell: '2'+  number: '1.996482967874904255590456922181224320635491112691848421532907427366799975400167532130410238462241788'+  comment: The root is $\xi_{4,2}=7.90767401912$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $1.9964829679$ to ten decimal+    places, in their row $\ell=3$ CITE{DGMMPR}.+- params:+    k: '4'+    ell: '3'+  number: '2.999385430194753174648485489376002505168401766875443841946011174195225771390338409594536448433558012'+  comment: The root is $\xi_{4,3}=11.9784075455$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $2.9993854302$ to ten decimal+    places, in their row $\ell=4$ CITE{DGMMPR}.+- params:+    k: '4'+    ell: '4'+  number: '3.999888264401298625623716085385569302254757474770833785533500959000231837332101924715416151887876541'+  comment: The root is $\xi_{4,4}=15.9950645692$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $3.9998882644$ to ten decimal+    places, in their row $\ell=5$ CITE{DGMMPR}.+- params:+    k: '4'+    ell: '5'+  number: '4.999979340653780324015040271985280966678004171623991495353210876623953329564676405924425455414668172'+  comment: The root is $\xi_{4,5}=19.9988997920$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $4.9999793407$ to ten decimal+    places, in their row $\ell=6$ CITE{DGMMPR}.+- params:+    k: '4'+    ell: '6'+  number: '5.999996141669181155871597337336411049803539145537996667408937848891236217991012208136281982868419701'+  comment: The root is $\xi_{4,6}=23.9997594760$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $5.9999961417$ to ten decimal+    places, in their row $\ell=7$ CITE{DGMMPR}.+- params:+    k: '5'+    ell: '1'+  number: '0.9924383912621006266589799793323504474696379410861973127564646960469684573473547755463108213196347197'+  comment: The root is $\xi_{5,1}=4.80100754972$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $0.9924383913$ to ten decimal+    places, in their row $\ell=2$ CITE{DGMMPR}.+- params:+    k: '5'+    ell: '2'+  number: '1.999448720069167727035462452430890911219734312410759174202843038368849831099715743153895577726858020'+  comment: The root is $\xi_{5,2}=9.97686430376$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $1.9994487201$ to ten decimal+    places, in their row $\ell=3$ CITE{DGMMPR}.+- params:+    k: '5'+    ell: '3'+  number: '2.999955435986581283444882025861140029212235129352555607766174797971254268977323520381948678026994564'+  comment: The root is $\xi_{5,3}=14.9974135011$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $2.9999554360$ to ten decimal+    places, in their row $\ell=4$ CITE{DGMMPR}.+- params:+    k: '5'+    ell: '4'+  number: '3.999996294949884624578061459731097323358511021420873096209477276474375757812738642334538931186731699'+  comment: The root is $\xi_{5,4}=19.9997251182$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $3.9999962949$ to ten decimal+    places, in their row $\ell=5$ CITE{DGMMPR}.+- params:+    k: '5'+    ell: '5'+  number: '4.999999687144044935393004612122874995112819585886125524372482323757480469448639156438469831161723458'+  comment: The root is $\xi_{5,5}=24.9999717443$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $4.9999996871$ to ten decimal+    places, in their row $\ell=6$ CITE{DGMMPR}.+- params:+    k: '5'+    ell: '6'+  number: '5.999999973288070189344630169624282144471417524844188007104938074752013814242184279230818936470510109'+  comment: The root is $\xi_{5,6}=29.9999971576$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $5.9999999733$ to ten decimal+    places, in their row $\ell=7$ CITE{DGMMPR}.+- params:+    k: '6'+    ell: '1'+  number: '0.9973795527786723480335298422727171806947578778455543989561183255629649006299375198226788332339351435'+  comment: The root is $\xi_{6,1}=5.90300005895$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $0.9973795528$ to ten decimal+    places, in their row $\ell=2$ CITE{DGMMPR}.+- params:+    k: '6'+    ell: '2'+  number: '1.999913747274470569389203571194216178672545088774116087666894883932989594152160007511452788301799383'+  comment: The root is $\xi_{6,2}=11.9946673302$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $1.9999137473$ to ten decimal+    places, in their row $\ell=3$ CITE{DGMMPR}.+- params:+    k: '6'+    ell: '3'+  number: '2.999996938381392376166114080230759591446494821958184942602793484833624392217738417863842320763123313'+  comment: The root is $\xi_{6,3}=17.9997334764$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $2.9999969384$ to ten decimal+    places, in their row $\ell=4$ CITE{DGMMPR}.+- params:+    k: '6'+    ell: '4'+  number: '3.999999888406371084509335436360640386934357548882021175485654372098562018995608685170457404864787032'+  comment: The root is $\xi_{6,4}=23.9999874749$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $3.9999998884$ to ten decimal+    places, in their row $\ell=5$ CITE{DGMMPR}.+- params:+    k: '6'+    ell: '5'+  number: '4.999999995861590166870067525133864208054376575359364102679230293551259772110190725782355071738634683'+  comment: The root is $\xi_{6,5}=29.9999994315$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $4.9999999959$ to ten decimal+    places, in their row $\ell=6$ CITE{DGMMPR}.+- params:+    k: '6'+    ell: '6'+  number: '5.999999999844601525039783111270085128864107889601055476101178401557652034751144040313008304160799203'+  comment: The root is $\xi_{6,6}=35.9999999748$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $5.9999999998$ to ten decimal+    places, in their row $\ell=7$ CITE{DGMMPR}.+- params:+    k: '7'+    ell: '1'+  number: '0.9990637587536802554886204642246230679289335411670661479087836641414840208770255075157509128677423698'+  comment: The root is $\xi_{7,1}=6.95345571335$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $0.9990637588$ to ten decimal+    places, in their row $\ell=2$ CITE{DGMMPR}.+- params:+    k: '7'+    ell: '2'+  number: '1.999986687836687466950470587085335927493710868623333718272369205851493375468424258861673415106998570'+  comment: The root is $\xi_{7,2}=13.9988580111$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $1.9999866878$ to ten decimal+    places, in their row $\ell=3$ CITE{DGMMPR}.+- params:+    k: '7'+    ell: '3'+  number: '2.999999798680631383681506245979015437628672628527238313672554169466675616181099647014632561347735652'+  comment: The root is $\xi_{7,3}=20.9999754217$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $2.9999997987$ to ten decimal+    places, in their row $\ell=4$ CITE{DGMMPR}.+- params:+    k: '7'+    ell: '4'+  number: '3.999999996867315061289050889484635088186412202341732709029986353874089772248409984224769542211257305'+  comment: The root is $\xi_{7,4}=27.9999995042$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $3.9999999969$ to ten decimal+    places, in their row $\ell=5$ CITE{DGMMPR}.+- params:+    k: '7'+    ell: '5'+  number: '4.999999999950315548351608834679948584474362081028250371712909868496022726268460193912208464051416812'+  comment: The root is $\xi_{7,5}=34.9999999903$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $5.0000000000$ to ten decimal+    places, in their row $\ell=6$ CITE{DGMMPR}.+- params:+    k: '7'+    ell: '6'+  number: '5.999999999999201282346480310860476468816909975235103544967261611856032007090916908596965754574630631'+  comment: The root is $\xi_{7,6}=41.9999999998$. Dietzfelbinger, Goerdt, Mitzenmacher,+    Montanari, Pagh and Rink tabulate this value as $6.0000000000$ to ten decimal+    places, in their row $\ell=7$ CITE{DGMMPR}.