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History of Ehrhart polynomials of the hypersimplices

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2026-09-15 21:49 bmatschke the k column showed the polynomial's name rather than k: every entry carried a param-latex overriding the label of its own parameter group, so the second column read $L_{\Delta(2,4)}(t)$ where it should read 2. The name it gave is the column header already, specialised to that row. current reviewed
2026-09-15 08:49 zeta3 hypersimplex Ehrhart polynomials
2026-09-15 08:48 zeta3 split hypersimplex polynomial quantities
2026-09-15 08:17 zeta3 update Birkhoff split cross-references
2026-09-13 20:18 zeta3 support hypersimplex search terms and lattice convention
2026-09-13 19:59 zeta3 initialize Sage in hypersimplex program snippet
2026-09-13 19:58 zeta3 with codex-cli hypersimplex Ehrhart and h-star polynomials
2026-09-13 19:53 zeta3 claim hypersimplex Ehrhart polynomial draft

What changed between 2026-09-15 08:49 and 2026-09-15 21:49

from line 82 (52 lines, 16 fewer than before) @@ -82,68 +82,52 @@ 
     '2':       number: 2/3*t^3 + 2*t^2 + 7/3*t + 1-      param-latex: $L_{\Delta(2,4)}(t)$   '5':     '2':       number: 11/24*t^4 + 25/12*t^3 + 85/24*t^2 + 35/12*t + 1-      param-latex: $L_{\Delta(2,5)}(t)$   '6':     '2':       number: 13/60*t^5 + 3/2*t^4 + 47/12*t^3 + 5*t^2 + 101/30*t + 1-      param-latex: $L_{\Delta(2,6)}(t)$     '3':       number: 11/20*t^5 + 11/4*t^4 + 23/4*t^3 + 25/4*t^2 + 37/10*t + 1-      param-latex: $L_{\Delta(3,6)}(t)$   '7':     '2':       number: 19/240*t^6 + 63/80*t^5 + 49/16*t^4 + 287/48*t^3 + 763/120*t^2 + 56/15*t         + 1-      param-latex: $L_{\Delta(2,7)}(t)$     '3':       number: 151/360*t^6 + 161/60*t^5 + 259/36*t^4 + 21/2*t^3 + 3199/360*t^2 + 259/60*t         + 1-      param-latex: $L_{\Delta(3,7)}(t)$   '8':     '2':       number: 1/42*t^7 + 29/90*t^6 + 53/30*t^5 + 91/18*t^4 + 49/6*t^3 + 343/45*t^2         + 283/70*t + 1-      param-latex: $L_{\Delta(2,8)}(t)$     '3':       number: 397/1680*t^7 + 359/180*t^6 + 281/40*t^5 + 245/18*t^4 + 1273/80*t^3 +         2051/180*t^2 + 2027/420*t + 1-      param-latex: $L_{\Delta(3,8)}(t)$     '4':       number: 151/315*t^7 + 151/45*t^6 + 463/45*t^5 + 161/9*t^4 + 862/45*t^3 + 574/45*t^2         + 533/105*t + 1-      param-latex: $L_{\Delta(4,8)}(t)$   '9':     '2':       number: 247/40320*t^8 + 121/1120*t^7 + 763/960*t^6 + 253/80*t^5 + 14203/1920*t^4         + 1667/160*t^3 + 88721/10080*t^2 + 1207/280*t + 1-      param-latex: $L_{\Delta(2,9)}(t)$     '3':       number: 477/4480*t^8 + 1311/1120*t^7 + 1731/320*t^6 + 1107/80*t^5 + 13899/640*t^4         + 3477/160*t^3 + 15419/1120*t^2 + 1473/280*t + 1-      param-latex: $L_{\Delta(3,9)}(t)$     '4':       number: 15619/40320*t^8 + 3607/1120*t^7 + 11311/960*t^6 + 1991/80*t^5 + 63991/1920*t^4         + 4669/160*t^3 + 166337/10080*t^2 + 1599/280*t + 1-      param-latex: $L_{\Delta(4,9)}(t)$   '10':     '2':       number: 251/181440*t^9 + 31/1008*t^8 + 1765/6048*t^7 + 37/24*t^6 + 42863/8640*t^5         + 481/48*t^4 + 115205/9072*t^3 + 4993/504*t^2 + 5729/1260*t + 1-      param-latex: $L_{\Delta(2,10)}(t)$     '3':       number: 913/22680*t^9 + 1135/2016*t^8 + 5071/1512*t^7 + 179/16*t^6 + 3128/135*t^5         + 2999/96*t^4 + 63041/2268*t^3 + 8069/504*t^2 + 3553/630*t + 1-      param-latex: $L_{\Delta(3,10)}(t)$     '4':       number: 44117/181440*t^9 + 2489/1008*t^8 + 66547/6048*t^7 + 683/24*t^6 + 409361/8640*t^5         + 2543/48*t^4 + 363947/9072*t^3 + 10127/504*t^2 + 7883/1260*t + 1-      param-latex: $L_{\Delta(4,10)}(t)$     '5':       number: 15619/36288*t^9 + 15619/4032*t^8 + 94939/6048*t^7 + 3607/96*t^6 + 101311/1728*t^5         + 11911/192*t^4 + 25394/567*t^3 + 21689/1008*t^2 + 1627/252*t + 1-      param-latex: $L_{\Delta(5,10)}(t)$   '11':     '2':
from line 135 (16 lines, 4 fewer than before) @@ -151,20 +135,16 @@ 
         + 447689/172800*t^6 + 246697/34560*t^5 + 14597/1134*t^4 + 543763/36288*t^3         + 91949/8400*t^2 + 1199/252*t + 1-      param-latex: $L_{\Delta(2,11)}(t)$     '3':       number: 299/22680*t^10 + 16621/72576*t^9 + 41591/24192*t^8 + 88693/12096*t^7         + 170137/8640*t^6 + 604109/17280*t^5 + 3043997/72576*t^4 + 308473/9072*t^3         + 60929/3360*t^2 + 15059/2520*t + 1-      param-latex: $L_{\Delta(3,11)}(t)$     '4':       number: 56899/453600*t^10 + 565631/362880*t^9 + 205733/24192*t^8 + 326491/12096*t^7         + 2400629/43200*t^6 + 1348787/17280*t^5 + 5535695/72576*t^4 + 468655/9072*t^3         + 1185701/50400*t^2 + 16973/2520*t + 1-      param-latex: $L_{\Delta(4,11)}(t)$     '5':       number: 655177/1814400*t^10 + 336083/90720*t^9 + 2078791/120960*t^8 + 287639/6048*t^7         + 7525771/86400*t^6 + 95557/864*t^5 + 35914087/362880*t^4 + 1125575/18144*t^3         + 443179/16800*t^2 + 17897/2520*t + 1-      param-latex: $L_{\Delta(5,11)}(t)$   '12':     '2':
from line 152 (20 lines, 5 fewer than before) @@ -172,25 +152,20 @@ 
         + 332249/302400*t^7 + 18997/4800*t^6 + 876959/90720*t^5 + 80179/5040*t^4 +         244681/14175*t^3 + 150293/12600*t^2 + 68591/13860*t + 1-      param-latex: $L_{\Delta(2,12)}(t)$     '3':       number: 50879/13305600*t^11 + 6979/86400*t^10 + 60271/80640*t^9 + 32153/8064*t^8         + 5483809/403200*t^7 + 897259/28800*t^6 + 11875111/241920*t^5 + 185339/3456*t^4         + 451173/11200*t^3 + 338503/16800*t^2 + 58007/9240*t + 1-      param-latex: $L_{\Delta(3,12)}(t)$     '4':       number: 1093/19800*t^11 + 62879/75600*t^10 + 20893/3780*t^9 + 10813/504*t^8         + 684323/12600*t^7 + 340967/3600*t^6 + 5258/45*t^5 + 38819/378*t^4 + 1202029/18900*t^3         + 42218/1575*t^2 + 1103/154*t + 1-      param-latex: $L_{\Delta(4,12)}(t)$     '5':       number: 1623019/6652800*t^11 + 882773/302400*t^10 + 1908073/120960*t^9 + 1028401/20160*t^8         + 7395023/67200*t^7 + 2401619/14400*t^6 + 4398559/24192*t^5 + 8661917/60480*t^4         + 12163441/151200*t^3 + 782969/25200*t^2 + 8861/1155*t + 1-      param-latex: $L_{\Delta(5,12)}(t)$     '6':       number: 655177/1663200*t^11 + 655177/151200*t^10 + 5507/252*t^9 + 336083/5040*t^8         + 6898277/50400*t^7 + 1430341/7200*t^6 + 3152491/15120*t^5 + 1200463/7560*t^4         + 30291/350*t^3 + 68321/2100*t^2 + 18107/2310*t + 1-      param-latex: $L_{\Delta(6,12)}(t)$   '13':     '2':
from line 174 (4 lines, 1 fewer than before) @@ -199,5 +174,4 @@ 
         + 69295109/3628800*t^4 + 35417369/1814400*t^3 + 1018381/79200*t^2 + 35503/6930*t         + 1-      param-latex: $L_{\Delta(2,13)}(t)$     '3':       number: 478271/479001600*t^12 + 2010749/79833600*t^11 + 12264473/43545600*t^10
from line 179 (4 lines, 1 fewer than before) @@ -205,5 +179,4 @@ 
         + 94940131/1451520*t^5 + 719975269/10886400*t^4 + 28178267/604800*t^3 + 18350293/831600*t^2         + 60541/9240*t + 1-      param-latex: $L_{\Delta(3,13)}(t)$     '4':       number: 226393/10644480*t^12 + 408395/1064448*t^11 + 8921861/2903040*t^10 +
from line 184 (4 lines, 1 fewer than before) @@ -211,5 +184,4 @@ 
         + 79099241/483840*t^5 + 95648839/725760*t^4 + 27503801/362880*t^3 + 1106599/36960*t^2         + 104611/13860*t + 1-      param-latex: $L_{\Delta(4,13)}(t)$     '5':       number: 11053079/79833600*t^12 + 25873471/13305600*t^11 + 89444797/7257600*t^10
from line 189 (4 lines, 1 fewer than before) @@ -217,5 +189,4 @@ 
         + 13183313/48384*t^5 + 87953099/453600*t^4 + 90426167/907200*t^3 + 19728683/554400*t^2         + 226811/27720*t + 1-      param-latex: $L_{\Delta(5,13)}(t)$     '6':       number: 27085381/79833600*t^12 + 55168451/13305600*t^11 + 11280737/483840*t^10
from line 194 (4 lines, 1 fewer than before) @@ -223,5 +194,4 @@ 
         + 27715103/80640*t^5 + 7768501/33600*t^4 + 102484187/907200*t^3 + 4270747/110880*t^2         + 235391/27720*t + 1-      param-latex: $L_{\Delta(6,13)}(t)$   '14':     '2':
from line 200 (4 lines, 1 fewer than before) @@ -230,5 +200,4 @@ 
         + 4060727/259200*t^5 + 8711729/388800*t^4 + 1550689/71280*t^3 + 408161/29700*t^2         + 951953/180180*t + 1-      param-latex: $L_{\Delta(2,14)}(t)$     '3':       number: 82207/345945600*t^13 + 241177/34214400*t^12 + 1068137/11404800*t^11
from line 205 (4 lines, 1 fewer than before) @@ -236,5 +205,4 @@ 
         + 197267941/3110400*t^6 + 43426663/518400*t^5 + 15421757/194400*t^4 + 25135273/475200*t^3         + 5677373/237600*t^2 + 272401/40040*t + 1-      param-latex: $L_{\Delta(3,14)}(t)$     '4':       number: 910669/124540416*t^13 + 2666489/17107200*t^12 + 50860811/34214400*t^11
from line 210 (4 lines, 1 fewer than before) @@ -242,5 +210,4 @@ 
         + 331357247/1555200*t^6 + 33840991/155520*t^5 + 63442561/388800*t^4 + 15706253/178200*t^3         + 1956773/59400*t^2 + 355804/45045*t + 1-      param-latex: $L_{\Delta(4,14)}(t)$     '5':       number: 28218769/415134720*t^13 + 25502053/22809600*t^12 + 189526301/22809600*t^11
from line 215 (4 lines, 1 fewer than before) @@ -248,5 +215,4 @@ 
         + 901850989/2073600*t^6 + 79259561/207360*t^5 + 129706447/518400*t^4 + 340659967/2851200*t^3         + 395317/9900*t^2 + 3115129/360360*t + 1-      param-latex: $L_{\Delta(5,14)}(t)$     '6':       number: 125468459/518918400*t^13 + 635641/190080*t^12 + 121304801/5702400*t^11
from line 220 (4 lines, 1 fewer than before) @@ -254,5 +220,4 @@ 
         + 11012027/17280*t^6 + 4188971/8100*t^5 + 4081337/12960*t^4 + 50182301/356400*t^3         + 175487/3960*t^2 + 1635857/180180*t + 1-      param-latex: $L_{\Delta(6,14)}(t)$     '7':       number: 27085381/74131200*t^13 + 27085381/5702400*t^12 + 242237/8448*t^11 +
from line 225 (4 lines, 1 fewer than before) @@ -260,5 +225,4 @@ 
         + 372761233/518400*t^6 + 5463163/9600*t^5 + 5487443/16200*t^4 + 21146681/142560*t^3         + 604643/13200*t^2 + 237371/25740*t + 1-      param-latex: $L_{\Delta(7,14)}(t)$   '15':     '2':
from line 231 (4 lines, 1 fewer than before) @@ -267,5 +231,4 @@ 
         + 22068727/5806080*t^7 + 62234543/6220800*t^6 + 3957619/207360*t^5 + 618362471/23950080*t^4         + 1708009/71280*t^3 + 1103807123/75675600*t^2 + 978683/180180*t + 1-      param-latex: $L_{\Delta(2,15)}(t)$     '3':       number: 252073/4843238400*t^14 + 1409/786240*t^13 + 7067/253440*t^12 + 197077/760320*t^11
from line 236 (4 lines, 1 fewer than before) @@ -273,5 +236,4 @@ 
         + 19422619/230400*t^6 + 7190401/69120*t^5 + 247756151/2661120*t^4 + 37869/640*t^3         + 26951489/1051050*t^2 + 120719/17160*t + 1-      param-latex: $L_{\Delta(3,15)}(t)$     '4':       number: 14172199/6227020800*t^14 + 839521/14826240*t^13 + 4345531/6842880*t^12
from line 241 (4 lines, 1 fewer than before) @@ -279,5 +241,4 @@ 
         + 335428619/1451520*t^7 + 1824926437/6220800*t^6 + 11561527/41472*t^5 + 672384883/3421440*t^4         + 57344251/570240*t^3 + 774504587/21621600*t^2 + 1481341/180180*t + 1-      param-latex: $L_{\Delta(4,15)}(t)$     '5':       number: 102869687/3487131648*t^14 + 93762997/166053888*t^13 + 26814797/5474304*t^12
from line 246 (4 lines, 1 fewer than before) @@ -285,5 +246,4 @@ 
         + 685133401/1161216*t^7 + 156630283/248832*t^6 + 7056737/13824*t^5 + 1491723449/4790016*t^4         + 7964861/57024*t^3 + 267071513/6054048*t^2 + 653483/72072*t + 1-      param-latex: $L_{\Delta(5,15)}(t)$     '6':       number: 1427029207/9686476800*t^14 + 642967681/276756480*t^13 + 17069149/1013760*t^12
from line 252 (4 lines, 1 fewer than before) @@ -292,5 +252,4 @@ 
         12594131/17280*t^5 + 543799349/1330560*t^4 + 1194569/7040*t^3 + 839599363/16816800*t^2         + 28867/3003*t + 1-      param-latex: $L_{\Delta(6,15)}(t)$     '7':       number: 2330931341/7264857600*t^14 + 52511021/11531520*t^13 + 24030767/798336*t^12
from line 257 (4 lines, 1 fewer than before) @@ -298,5 +257,4 @@ 
         + 1267493/960*t^7 + 8815476293/7257600*t^6 + 29744423/34560*t^5 + 185254967/399168*t^4         + 5888683/31680*t^3 + 2669409121/50450400*t^2 + 237371/24024*t + 1-      param-latex: $L_{\Delta(7,15)}(t)$   '16':     '2':
from line 264 (4 lines, 1 fewer than before) @@ -306,5 +264,4 @@ 
         + 21939781/748440*t^4 + 9890467843/378378000*t^3 + 291201101/18918900*t^2         + 200713/36036*t + 1-      param-latex: $L_{\Delta(2,16)}(t)$     '3':       number: 13824739/1307674368000*t^15 + 4553683/10897286400*t^14 + 6386407/849139200*t^13
from line 270 (4 lines, 1 fewer than before) @@ -313,5 +270,4 @@ 
         + 18717373/172800*t^6 + 45279007097/359251200*t^5 + 160705799/1496880*t^4         + 53994658409/825552000*t^3 + 2067214613/75675600*t^2 + 290287/40040*t + 1-      param-latex: $L_{\Delta(3,16)}(t)$     '4':       number: 26502841/40864824000*t^15 + 2029481/108972864*t^14 + 283464119/1167566400*t^13
from line 276 (4 lines, 1 fewer than before) @@ -320,5 +276,4 @@ 
         + 2095357/5400*t^6 + 1945534273/5613300*t^5 + 86651311/374220*t^4 + 1781677097/15765750*t^3         + 182499931/4729725*t^2 + 767549/90090*t + 1-      param-latex: $L_{\Delta(4,16)}(t)$     '5':       number: 15041229521/1307674368000*t^15 + 2770152961/10897286400*t^14 + 23879655967/9340531200*t^13
from line 283 (4 lines, 1 fewer than before) @@ -328,5 +283,4 @@ 
         + 1454152371601/9081072000*t^3 + 3643452523/75675600*t^2 + 3407689/360360*t         + 1-      param-latex: $L_{\Delta(5,16)}(t)$     '6':       number: 6423562433/81729648000*t^15 + 7707502519/5448643200*t^14 + 27326623759/2335132800*t^13
from line 289 (4 lines, 1 fewer than before) @@ -335,5 +289,4 @@ 
         + 138967777/97200*t^6 + 5489557519/5613300*t^5 + 127591193/249480*t^4 + 226264391791/1135134000*t^3         + 349085689/6306300*t^2 + 17335/1716*t + 1-      param-latex: $L_{\Delta(6,16)}(t)$     '7':       number: 103795866137/435891456000*t^15 + 2720962597/726485760*t^14 + 85436922007/3113510400*t^13
from line 296 (4 lines, 1 fewer than before) @@ -343,5 +296,4 @@ 
         + 2044084141171/9081072000*t^3 + 301806581/5045040*t^2 + 755383/72072*t +         1-      param-latex: $L_{\Delta(7,16)}(t)$     '8':       number: 2330931341/6810804000*t^15 + 2330931341/454053600*t^14 + 7024858627/194594400*t^13
from line 302 (4 lines, 1 fewer than before) @@ -350,5 +302,4 @@ 
         + 1224216929/935550*t^5 + 13293361/20790*t^4 + 16605427634/70945875*t^3 +         96698018/1576575*t^2 + 95549/9009*t + 1-      param-latex: $L_{\Delta(8,16)}(t)$   '17':     '2':
from line 310 (4 lines, 1 fewer than before) @@ -359,5 +310,4 @@ 
         + 4776994588679/145297152000*t^4 + 10484040029/370656000*t^3 + 3261990821/201801600*t^2         + 4107353/720720*t + 1-      param-latex: $L_{\Delta(2,17)}(t)$     '3':       number: 8386549/4184557977600*t^16 + 235577347/2615348736000*t^15 + 1941159433/1046139494400*t^14
from line 317 (4 lines, 1 fewer than before) @@ -367,5 +317,4 @@ 
         + 10638261256487/87178291200*t^4 + 1300144121167/18162144000*t^3 + 17510765017/605404800*t^2         + 1789913/240240*t + 1-      param-latex: $L_{\Delta(3,17)}(t)$     '4':       number: 238139017/1394852659200*t^16 + 4884188689/871782912000*t^15 + 2663021831/31701196800*t^14
from line 324 (4 lines, 1 fewer than before) @@ -375,5 +324,4 @@ 
         + 28323235169/105670656*t^4 + 2278299817967/18162144000*t^3 + 924827489/22422400*t^2         + 1268081/144144*t + 1-      param-latex: $L_{\Delta(4,17)}(t)$     '5':       number: 12197605507/2988969984000*t^16 + 38588349623/373621248000*t^15 + 178582288211/149448499200*t^14
from line 331 (4 lines, 1 fewer than before) @@ -383,5 +331,4 @@ 
         + 27785051592401/62270208000*t^4 + 5789518963/32032000*t^3 + 4500237263/86486400*t^2         + 7075451/720720*t + 1-      param-latex: $L_{\Delta(5,17)}(t)$     '6':       number: 782115518299/20922789888000*t^16 + 2002909883633/2615348736000*t^15
from line 338 (4 lines, 1 fewer than before) @@ -391,5 +338,4 @@ 
         + 907747514761/718502400*t^5 + 90389584514179/145297152000*t^4 + 4168694454773/18162144000*t^3         + 12230913041/201801600*t^2 + 2535431/240240*t + 1-      param-latex: $L_{\Delta(6,17)}(t)$     '7':       number: 3207483178157/20922789888000*t^16 + 7040798154763/2615348736000*t^15
from line 345 (4 lines, 1 fewer than before) @@ -399,5 +345,4 @@ 
         + 168771140057/102643200*t^5 + 110678531004277/145297152000*t^4 + 1607840669861/6054048000*t^3         + 13427417207/201801600*t^2 + 1590299/144144*t + 1-      param-latex: $L_{\Delta(7,17)}(t)$     '8':       number: 12157712239/39852933120*t^16 + 4300583023337/871782912000*t^15 + 13073198753273/348713164800*t^14
from line 352 (4 lines, 1 fewer than before) @@ -407,5 +352,4 @@ 
         + 3481763779513/4151347200*t^4 + 5170327419391/18162144000*t^3 + 2807586737/40360320*t^2         + 1624333/144144*t + 1-      param-latex: $L_{\Delta(8,17)}(t)$   '18':     '2':
from line 360 (4 lines, 1 fewer than before) @@ -416,5 +360,4 @@ 
         + 37302932341/1213056000*t^5 + 26014811/712800*t^4 + 138029148779/4540536000*t^3         + 284302033/16816800*t^2 + 35655743/6126120*t + 1-      param-latex: $L_{\Delta(2,18)}(t)$     '3':       number: 704339/1976041267200*t^17 + 68179/3773952000*t^16 + 61326743/145297152000*t^15
from line 367 (4 lines, 1 fewer than before) @@ -424,5 +367,4 @@ 
         + 141092116799/807206400*t^5 + 3591628709/26208000*t^4 + 13067695063/168168000*t^3         + 7763713/254800*t^2 + 1949768/255255*t + 1-      param-latex: $L_{\Delta(3,18)}(t)$     '4':       number: 297507989/7113748561920*t^17 + 1807009/1162377216*t^16 + 2104789937/79252992000*t^15
from line 374 (4 lines, 1 fewer than before) @@ -432,5 +374,4 @@ 
         + 1189860677519/2377589760*t^5 + 3856498909/12612600*t^4 + 625827521629/4540536000*t^3         + 2210167433/50450400*t^2 + 55482673/6126120*t + 1-      param-latex: $L_{\Delta(4,18)}(t)$     '5':       number: 23667665053/17784371404800*t^17 + 22238830951/581188608000*t^16 + 220257696289/435891456000*t^15
from line 381 (4 lines, 1 fewer than before) @@ -440,5 +381,4 @@ 
         + 65241406255889/65383718400*t^5 + 6281184766093/12108096000*t^4 + 83147049481/412776000*t^3         + 255870553/4586400*t^2 + 2221493/218790*t + 1-      param-latex: $L_{\Delta(5,18)}(t)$     '6':       number: 317627331799/19760412672000*t^17 + 54218672303/145297152000*t^16 + 1161028375763/290594304000*t^15
from line 388 (4 lines, 1 fewer than before) @@ -448,5 +388,4 @@ 
         + 12784002957967/8072064000*t^5 + 93311811071/126126000*t^4 + 43742812109/168168000*t^3         + 73652279/1121120*t^2 + 22408157/2042040*t + 1-      param-latex: $L_{\Delta(6,18)}(t)$     '7':       number: 7763913237097/88921857024000*t^17 + 166233279019/96864768000*t^16 +
from line 396 (4 lines, 1 fewer than before) @@ -457,5 +396,4 @@ 
         + 278824725719/908107200*t^3 + 368595853/5045040*t^2 + 8839451/765765*t +         1-      param-latex: $L_{\Delta(7,18)}(t)$     '8':       number: 8313722318537/35568742809600*t^17 + 599392631477/145297152000*t^16 +
from line 404 (4 lines, 1 fewer than before) @@ -466,5 +404,4 @@ 
         + 218735303519/648648000*t^3 + 3914455513/50450400*t^2 + 14554933/1225224*t         + 1-      param-latex: $L_{\Delta(8,18)}(t)$     '9':       number: 12157712239/37638881280*t^17 + 12157712239/2214051840*t^16 + 4270327196879/96864768000*t^15
from line 411 (4 lines, 1 fewer than before) @@ -474,5 +411,4 @@ 
         + 13667854873/5125120*t^5 + 28325682897/25625600*t^4 + 38971831489/112112000*t^3         + 887003237/11211200*t^2 + 1632341/136136*t + 1-      param-latex: $L_{\Delta(9,18)}(t)$   '19':     '2':
from line 420 (4 lines, 1 fewer than before) @@ -484,5 +420,4 @@ 
         + 589936188311/18162144000*t^3 + 11333378761/643242600*t^2 + 36356443/6126120*t         + 1-      param-latex: $L_{\Delta(2,19)}(t)$     '3':       number: 95609981/1600593426432000*t^18 + 1205664703/355687428096000*t^17 + 5593238411/62768369664000*t^16
from line 428 (4 lines, 1 fewer than before) @@ -493,5 +428,4 @@ 
         + 199224188101073/1307674368000*t^4 + 507097796243/6054048000*t^3 + 89705061133/2806876800*t^2         + 95756029/12252240*t + 1-      param-latex: $L_{\Delta(3,19)}(t)$     '4':       number: 614033131/64023737057280*t^18 + 28504142893/71137485619200*t^17 + 485453440957/62768369664000*t^16
from line 436 (4 lines, 1 fewer than before) @@ -502,5 +436,4 @@ 
         + 450597042770551/1307674368000*t^4 + 2727132028483/18162144000*t^3 + 1428986729017/30875644800*t^2         + 37983109/4084080*t + 1-      param-latex: $L_{\Delta(4,19)}(t)$     '5':       number: 59606993/148203095040*t^18 + 103070503441/7904165068800*t^17 + 123675281213/634023936000*t^16
from line 444 (4 lines, 1 fewer than before) @@ -511,5 +444,4 @@ 
         + 4034674669163/18162144000*t^3 + 67948416037/1143542400*t^2 + 128262749/12252240*t         + 1-      param-latex: $L_{\Delta(5,19)}(t)$     '6':       number: 722452584787/114328101888000*t^18 + 1200227144851/7258927104000*t^17
from line 452 (4 lines, 1 fewer than before) @@ -520,5 +452,4 @@ 
         + 32274549272437/37362124800*t^4 + 16776186971/57657600*t^3 + 8900240737/126023040*t^2         + 139250563/12252240*t + 1-      param-latex: $L_{\Delta(6,19)}(t)$     '7':       number: 2859970743073/64023737057280*t^18 + 69868595349463/71137485619200*t^17
from line 461 (4 lines, 1 fewer than before) @@ -530,5 +461,4 @@ 
         6342720401089/18162144000*t^3 + 2451483910867/30875644800*t^2 + 49084619/4084080*t         + 1-      param-latex: $L_{\Delta(7,19)}(t)$     '8':       number: 27964165775423/177843714048000*t^18 + 361610774423567/118562476032000*t^17
from line 470 (4 lines, 1 fewer than before) @@ -540,5 +470,4 @@ 
         + 567118716450961/435891456000*t^4 + 7106317213379/18162144000*t^3 + 175815722539/2058376320*t^2         + 152485811/12252240*t + 1-      param-latex: $L_{\Delta(8,19)}(t)$     '9':       number: 37307713155613/128047474114560*t^18 + 47031555912931/8892185702400*t^17
from line 478 (4 lines, 1 fewer than before) @@ -549,5 +478,4 @@ 
         + 237461864531083/65383718400*t^5 + 262103113599269/186810624000*t^4 + 2501882491093/6054048000*t^3         + 2731594237649/30875644800*t^2 + 31014479/2450448*t + 1-      param-latex: $L_{\Delta(9,19)}(t)$   '20':     '2':
from line 487 (4 lines, 1 fewer than before) @@ -559,5 +487,4 @@ 
         + 716983186781/16345929600*t^4 + 1332758314439/38594556000*t^3 + 141306446467/7718911200*t^2         + 234454999/38798760*t + 1-      param-latex: $L_{\Delta(2,20)}(t)$     '3':       number: 383925299/40548366802944000*t^19 + 382702049/640237370572800*t^18 +
from line 496 (4 lines, 1 fewer than before) @@ -569,5 +496,4 @@ 
         + 139952316011/1559376000*t^3 + 79317201431/2375049600*t^2 + 1858243391/232792560*t         + 1-      param-latex: $L_{\Delta(3,20)}(t)$     '4':       number: 17657989/8532905472000*t^19 + 321800797/3334569638400*t^18 + 9287523041/4446092851200*t^17
from line 504 (4 lines, 1 fewer than before) @@ -578,5 +504,4 @@ 
         + 1762678621/4586400*t^4 + 3133818853631/19297278000*t^3 + 2846174749/58476600*t^2         + 554616397/58198140*t + 1-      param-latex: $L_{\Delta(4,20)}(t)$     '5':       number: 9197440123/81096733605888*t^19 + 26364254107/6402373705728*t^18 + 492860313037/7113748561920*t^17
from line 512 (4 lines, 1 fewer than before) @@ -587,5 +512,4 @@ 
         + 8790062108029/13076743680*t^4 + 299910422587/1235025792*t^3 + 1494689587/23750496*t^2         + 27843779/2586584*t + 1-      param-latex: $L_{\Delta(5,20)}(t)$     '6':       number: 829745172187/362038989312000*t^19 + 5379045855709/80029671321600*t^18
from line 520 (4 lines, 1 fewer than before) @@ -596,5 +520,4 @@ 
         + 37972515708161/16345929600*t^5 + 4059566408461/4086482400*t^4 + 1035530065133/3216213000*t^3         + 13227990703/175429800*t^2 + 341417077/29099070*t + 1-      param-latex: $L_{\Delta(6,20)}(t)$     '7':       number: 10031448420143/482718652416000*t^19 + 27204534921281/53353114214400*t^18
from line 529 (4 lines, 1 fewer than before) @@ -606,5 +529,4 @@ 
         + 1052276154557/807206400*t^4 + 60509242143277/154378224000*t^3 + 220138221781/2572970400*t^2         + 1450653161/116396280*t + 1-      param-latex: $L_{\Delta(7,20)}(t)$     '8':       number: 21753114839033/230388447744000*t^19 + 20198547534727/10003708915200*t^18
from line 537 (4 lines, 1 fewer than before) @@ -615,5 +537,4 @@ 
         + 1389955462099/333590400*t^5 + 6376306892609/4086482400*t^4 + 111901277333/250614000*t^3         + 179541754627/1929727800*t^2 + 83892023/6466460*t + 1-      param-latex: $L_{\Delta(8,20)}(t)$     '9':       number: 515968158649877/2252687044608000*t^19 + 1436047812847939/320118685286400*t^18
from line 547 (4 lines, 1 fewer than before) @@ -626,5 +547,4 @@ 
         + 3536577750991/7351344000*t^3 + 1506987616129/15437822400*t^2 + 772605221/58198140*t         + 1-      param-latex: $L_{\Delta(9,20)}(t)$     '10':       number: 37307713155613/121645100408832*t^19 + 37307713155613/6402373705728*t^18
from line 556 (4 lines, 1 fewer than before) @@ -636,5 +556,4 @@ 
         + 76094572289/154378224*t^3 + 15307582769/154378224*t^2 + 155685007/11639628*t         + 1-      param-latex: $L_{\Delta(10,20)}(t)$ Data properties:   type: Q[]

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