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--- homogeneous_solutions [2023/02/18 20:49]
harshec
+++ homogeneous_solutions [2026/02/10 18:09] (current)
harshec
@@ Line 1: / Line 1: @@
 ====Solution Counts For Homogeneous Sets====
-These counts avoid equivalent sets where the dice are simply relabeled. In other words, these counts assume that in the string representation of a solution the first “a” appears before the first “b” which appears before the first “c”, and so on. The counts do allow for internal “redundancies” as defined by B. Hearn.
+These counts avoid equivalent sets where the dice are simply relabeled. In other words, these counts assume that in the string representation of a solution the first “a” appears before the first “b” which appears before the first “c”, and so on.
+Most of these numbers were calculated by Landon Kryger and Brandon Enright. Exceptions to this are noted in the footnotes.
 ===Legend===
@@ Line 25: / Line 27: @@
 |  18  | 24310 / 24310 / 24310  | 6521 / 767975 / 37978905250  | 1278 / 84588 / 893864677761053000  | x  | x  |
 |  24  | 1352078 / 1352078 / 1352078  | ? / 3163085576 / 564121960420200  | ? / ? / 9.82538756092255E+24  | x  | x  |
-|  30  | 77558760 / 77558760 / 77558760  | ? / ? / 8915829964229030000  | ? / ? / 1.1856736358608E+32 | ? / ? / 5.40670186413478E+46  | ? / ? / 4.12672592988253E+62  |
+|  30  | 77558760 / 77558760 / 77558760  | ? / 15050285682919 / 8915829964229030000  | ? / ? / 1.1856736358608E+32 | ? / ? / 5.40670186413478E+46  | ? / ? / 4.12672592988253E+62  |
 |  60  | 59132290782429200 / 59132290782429200 / 59132290782429200  | ? / ? / 1.32679649279208E+40  | ? / ? / 5.63043962364763E+67  | ? / ? / 3.62586633628878E+98  | ? / ? / 8.010847767853E+131  |
@@ Line 33: / Line 35: @@
 |  12  | 462 / 462 / 2048  | 317 / 11572 / 362797056  | 10 / 128 / 1521681143169020  | x  | x  |
 |  18  | 24310 / 24310 / 131072  | 18889 / 74646644 / 16926659444736  | 105 / 3828 / 2.90797794982684E+23  | x  | x  |
-|  24  | 1352078 / 1352078 / 8388608  | ? / ? / 789730223053611000  | ? / ? / 5.55723240354287E+31  | x  | x  |
+|  24  | 1352078 / 1352078 / 8388608  | ? / 1382404516 [1] / 789730223053611000  | ? / ? / 5.55723240354287E+31  | x  | x  |
 |  30  | 77558760 / 77558760 / 536870912  | ? / ? / 3.68456532867889E+22  | ? / ? / 1.06200365064067E+40  | ? / ? / 1.9781359483314E+60  | ? / ? / 7.28857113063509E+82  |
 |  60  | ? / ? / 576460752303421000  | ? / ? / 8.14561299678166E+45  | ? / ? / 2.70684420953785E+81  | ? / ? / 4.6956261960971E+122  | ? / ? / 3.8248753770958E+168  |
@@ Line 63: / Line 65: @@
 |  30  | 128 / 128 / 128  | ? / 0 / 279936  | ? / 0 / 4586471424  | ? / 0 / 358318080000000  | ? / 0 / 1.0030613004288E+20  |
 |  60  | 16384 / 16384 / 16384  | ? / 4132896768 / 78364164096  | ? / ? / 21035720123168500000  | ? / ? / 1.28391846454886E+29  | ? / ? / 1.00613197241791E+40  |
+[1] found by Kayla Toll

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