History of Ehrhart polynomials of the permutohedra

back to table · edit · history · where entries came from · files

compare when who what
2026-09-15 21:57 bmatschke interactive the n column showed the polynomial's name rather than n: a param-latex on every entry replaced the label of its own parameter group, so the column read $L_{\Pi_3}(t)$ where it should read 3. The header already says which polynomial. current reviewed
2026-09-15 09:04 zeta3 table-split@1.71+d0fe2dd9 attach Ehrhart-only generator
2026-09-15 09:04 zeta3 table-split@1.71+d0fe2dd9 split h-star polynomials into T245
2026-09-15 08:52 zeta3 interactive update T234 cross-reference after split
2026-09-13 20:54 zeta3 table-repair@1.103+ae5cb67d clarify the permutohedron order and Ehrhart-series conventions
2026-09-13 20:37 zeta3 table-build@1.118+dc6728ab add checked permutohedron table prose
2026-09-13 20:34 zeta3 table-build@1.118+dc6728ab add checked permutohedron table prose
2026-09-13 20:34 zeta3 with codex-cli table-build@1.118+dc6728ab permutohedron Ehrhart and h-star polynomials
2026-09-13 20:28 zeta3 table-build@1.118+dc6728ab claim permutohedron Ehrhart draft

What changed between 2026-09-15 09:04 and 2026-09-15 21:57

from line 97 (36 lines, 12 fewer than before) @@ -97,48 +97,36 @@
   '3':     number: 3*t^2 + 3*t + 1-    param-latex: $L_{\Pi_3}(t)$   '4':     number: 16*t^3 + 15*t^2 + 6*t + 1-    param-latex: $L_{\Pi_4}(t)$   '5':     number: 125*t^4 + 110*t^3 + 45*t^2 + 10*t + 1-    param-latex: $L_{\Pi_5}(t)$   '6':     number: 1296*t^5 + 1080*t^4 + 435*t^3 + 105*t^2 + 15*t + 1-    param-latex: $L_{\Pi_6}(t)$   '7':     number: 16807*t^6 + 13377*t^5 + 5250*t^4 + 1295*t^3 + 210*t^2 + 21*t + 1-    param-latex: $L_{\Pi_7}(t)$   '8':     number: 262144*t^7 + 200704*t^6 + 76608*t^5 + 18865*t^4 + 3220*t^3 + 378*t^2 +       28*t + 1-    param-latex: $L_{\Pi_8}(t)$   '9':     number: 4782969*t^8 + 3542940*t^7 + 1316574*t^6 + 320544*t^5 + 55755*t^4 + 7056*t^3       + 630*t^2 + 36*t + 1-    param-latex: $L_{\Pi_9}(t)$   '10':     number: 100000000*t^9 + 72000000*t^8 + 26100000*t^7 + 6258000*t^6 + 1092105*t^5       + 143325*t^4 + 14070*t^3 + 990*t^2 + 45*t + 1-    param-latex: $L_{\Pi_10}(t)$   '11':     number: 2357947691*t^10 + 1656409535*t^9 + 587030895*t^8 + 138437310*t^7 + 24048255*t^6       + 3207897*t^5 + 331485*t^4 + 26070*t^3 + 1485*t^2 + 55*t + 1-    param-latex: $L_{\Pi_11}(t)$   '12':     number: 61917364224*t^11 + 42568187904*t^10 + 14780620800*t^9 + 3428282880*t^8       + 590412240*t^7 + 79170399*t^6 + 8411634*t^5 + 705375*t^4 + 45540*t^3 + 2145*t^2       + 66*t + 1-    param-latex: $L_{\Pi_12}(t)$   '13':     number: 1792160394037*t^12 + 1208912928522*t^11 + 412069511139*t^10 + 94059655690*t^9       + 16027796070*t^8 + 2146836978*t^7 + 231354123*t^6 + 20151846*t^5 + 1402830*t^4       + 75790*t^3 + 3003*t^2 + 78*t + 1-    param-latex: $L_{\Pi_13}(t)$   '14':     number: 56693912375296*t^13 + 37603105146880*t^12 + 12604714327296*t^11 + 2833936641536*t^10       + 477411574640*t^9 + 63641666088*t^8 + 6899167275*t^7 + 614506893*t^6 + 44837793*t^5       + 2637635*t^4 + 121121*t^3 + 4095*t^2 + 91*t + 1-    param-latex: $L_{\Pi_14}(t)$   '15':     number: 1946195068359375*t^14 + 1271514111328125*t^13 + 419801484375000*t^12 +
from line 134 (4 lines, 1 fewer than before) @@ -146,5 +134,4 @@
       + 20073049425*t^7 + 1508782275*t^6 + 93783690*t^5 + 4729725*t^4 + 187005*t^3       + 5460*t^2 + 105*t + 1-    param-latex: $L_{\Pi_15}(t)$   '16':     number: 72057594037927936*t^15 + 46443371157258240*t^14 + 15123782440058880*t^13
from line 139 (4 lines, 1 fewer than before) @@ -152,5 +139,4 @@
       + 702495121185*t^8 + 53789959080*t^7 + 3467403940*t^6 + 186113928*t^5 + 8143590*t^4       + 280280*t^3 + 7140*t^2 + 120*t + 1-    param-latex: $L_{\Pi_16}(t)$   '17':     number: 2862423051509815793*t^16 + 1822442358054692408*t^15 + 586049426860524300*t^14
from line 145 (4 lines, 1 fewer than before) @@ -159,5 +145,4 @@
       + 7530498976*t^6 + 352975896*t^5 + 13536250*t^4 + 409360*t^3 + 9180*t^2 + 136*t       + 1-    param-latex: $L_{\Pi_17}(t)$   '18':     number: 121439531096594251776*t^17 + 76461926986744528896*t^16 + 24307340986526810112*t^15
from line 151 (4 lines, 1 fewer than before) @@ -166,5 +151,4 @@
       + 316658880252*t^7 + 15572652732*t^6 + 643493214*t^5 + 21816270*t^4 + 584460*t^3       + 11628*t^2 + 153*t + 1-    param-latex: $L_{\Pi_18}(t)$   '19':     number: 5480386857784802185939*t^18 + 3415753581721829617275*t^17 + 1074495780444130114509*t^16
from line 157 (4 lines, 1 fewer than before) @@ -173,5 +157,4 @@
       236503301350745*t^9 + 13915427604507*t^8 + 707994733680*t^7 + 30850128582*t^6       + 1132991622*t^5 + 34215390*t^4 + 817836*t^3 + 14535*t^2 + 171*t + 1-    param-latex: $L_{\Pi_19}(t)$   '20':     number: 262144000000000000000000*t^19 + 161873920000000000000000*t^18 + 50429952000000000000000*t^17
from line 164 (4 lines, 1 fewer than before) @@ -181,5 +164,4 @@
       + 58838794350*t^6 + 1934143380*t^5 + 52374450*t^4 + 1124040*t^3 + 17955*t^2       + 190*t + 1-    param-latex: $L_{\Pi_20}(t)$ Tags: - polynomial 

Sign in to restore an earlier version.