***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St001901 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. ----------------------------------------------------------------------------- References: [1] (service unreachable) [[MathSciNet:1984625]] ----------------------------------------------------------------------------- Code: def statistic(la): s = SymmetricFunctions(ZZ).s() return max(c for _, c in s.higher_lie_character(la)) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [2] => 1 [1,1] => 1 [3] => 1 [2,1] => 1 [1,1,1] => 1 [4] => 1 [3,1] => 1 [2,2] => 1 [2,1,1] => 1 [1,1,1,1] => 1 [5] => 1 [4,1] => 2 [3,2] => 1 [3,1,1] => 1 [2,2,1] => 1 [2,1,1,1] => 1 [1,1,1,1,1] => 1 [6] => 3 [5,1] => 3 [4,2] => 2 [4,1,1] => 2 [3,3] => 1 [3,2,1] => 3 [3,1,1,1] => 1 [2,2,2] => 1 [2,2,1,1] => 1 [2,1,1,1,1] => 1 [1,1,1,1,1,1] => 1 [7] => 5 [6,1] => 6 [5,2] => 4 [5,1,1] => 4 [4,3] => 3 [4,2,1] => 5 [4,1,1,1] => 2 [3,3,1] => 2 [3,2,2] => 2 [3,2,1,1] => 3 [3,1,1,1,1] => 1 [2,2,2,1] => 1 [2,2,1,1,1] => 1 [2,1,1,1,1,1] => 1 [1,1,1,1,1,1,1] => 1 [8] => 12 [7,1] => 13 [6,2] => 7 [6,1,1] => 8 [5,3] => 6 [5,2,1] => 9 [5,1,1,1] => 4 [4,4] => 3 [4,3,1] => 8 [4,2,2] => 3 [4,2,1,1] => 6 [4,1,1,1,1] => 2 [3,3,2] => 3 [3,3,1,1] => 3 [3,2,2,1] => 4 [3,2,1,1,1] => 3 [3,1,1,1,1,1] => 1 [2,2,2,2] => 1 [2,2,2,1,1] => 1 [2,2,1,1,1,1] => 1 [2,1,1,1,1,1,1] => 1 [1,1,1,1,1,1,1,1] => 1 [9] => 24 [8,1] => 27 [7,2] => 16 [7,1,1] => 16 [6,3] => 13 [6,2,1] => 18 [6,1,1,1] => 8 [5,4] => 11 [5,3,1] => 15 [5,2,2] => 6 [5,2,1,1] => 11 [5,1,1,1,1] => 4 [4,4,1] => 7 [4,3,2] => 10 [4,3,1,1] => 10 [4,2,2,1] => 8 [4,2,1,1,1] => 6 [4,1,1,1,1,1] => 2 [3,3,3] => 2 [3,3,2,1] => 7 [3,3,1,1,1] => 3 [3,2,2,2] => 2 [3,2,2,1,1] => 5 [3,2,1,1,1,1] => 3 [3,1,1,1,1,1,1] => 1 [2,2,2,2,1] => 1 [2,2,2,1,1,1] => 1 [2,2,1,1,1,1,1] => 1 [2,1,1,1,1,1,1,1] => 1 [1,1,1,1,1,1,1,1,1] => 1 [10] => 77 [9,1] => 86 [8,2] => 48 [8,1,1] => 48 [7,3] => 39 [7,2,1] => 55 [7,1,1,1] => 18 [6,4] => 32 [6,3,1] => 45 [6,2,2] => 16 [6,2,1,1] => 32 [6,1,1,1,1] => 8 [5,5] => 15 [5,4,1] => 38 [5,3,2] => 27 [5,3,1,1] => 27 [5,2,2,1] => 19 [5,2,1,1,1] => 12 [5,1,1,1,1,1] => 4 [4,4,2] => 12 [4,4,1,1] => 12 [4,3,3] => 12 [4,3,2,1] => 34 [4,3,1,1,1] => 11 [4,2,2,2] => 4 [4,2,2,1,1] => 12 [4,2,1,1,1,1] => 6 [4,1,1,1,1,1,1] => 2 [3,3,3,1] => 5 [3,3,2,2] => 6 [3,3,2,1,1] => 12 [3,3,1,1,1,1] => 3 [3,2,2,2,1] => 6 [3,2,2,1,1,1] => 5 [3,2,1,1,1,1,1] => 3 [3,1,1,1,1,1,1,1] => 1 [2,2,2,2,2] => 1 [2,2,2,2,1,1] => 1 [2,2,2,1,1,1,1] => 1 [2,2,1,1,1,1,1,1] => 1 [2,1,1,1,1,1,1,1,1] => 1 [1,1,1,1,1,1,1,1,1,1] => 1 [11] => 210 [10,1] => 231 [9,2] => 138 [9,1,1] => 138 [8,3] => 99 [8,2,1] => 155 [8,1,1,1] => 56 [7,4] => 83 [7,3,1] => 113 [7,2,2] => 46 [7,2,1,1] => 83 [7,1,1,1,1] => 18 [6,5] => 77 [6,4,1] => 97 [6,3,2] => 71 [6,3,1,1] => 71 [6,2,2,1] => 54 [6,2,1,1,1] => 36 [6,1,1,1,1,1] => 8 [5,5,1] => 46 [5,4,2] => 62 [5,4,1,1] => 62 [5,3,3] => 27 [5,3,2,1] => 85 [5,3,1,1,1] => 31 [5,2,2,2] => 11 [5,2,2,1,1] => 30 [5,2,1,1,1,1] => 12 [5,1,1,1,1,1,1] => 4 [4,4,3] => 25 [4,4,2,1] => 39 [4,4,1,1,1] => 14 [4,3,3,1] => 34 [4,3,2,2] => 28 [4,3,2,1,1] => 50 [4,3,1,1,1,1] => 11 [4,2,2,2,1] => 14 [4,2,2,1,1,1] => 13 [4,2,1,1,1,1,1] => 6 [4,1,1,1,1,1,1,1] => 2 [3,3,3,2] => 8 [3,3,3,1,1] => 8 [3,3,2,2,1] => 19 [3,3,2,1,1,1] => 13 [3,3,1,1,1,1,1] => 3 [3,2,2,2,2] => 2 [3,2,2,2,1,1] => 9 [3,2,2,1,1,1,1] => 5 [3,2,1,1,1,1,1,1] => 3 [3,1,1,1,1,1,1,1,1] => 1 [2,2,2,2,2,1] => 1 [2,2,2,2,1,1,1] => 1 [2,2,2,1,1,1,1,1] => 1 [2,2,1,1,1,1,1,1,1] => 1 [2,1,1,1,1,1,1,1,1,1] => 1 [1,1,1,1,1,1,1,1,1,1,1] => 1 [12] => 640 [11,1] => 700 [10,2] => 386 [10,1,1] => 384 [9,3] => 288 [9,2,1] => 428 [9,1,1,1] => 150 [8,4] => 246 [8,3,1] => 324 [8,2,2] => 113 [8,2,1,1] => 246 [8,1,1,1,1] => 56 [7,5] => 220 [7,4,1] => 280 [7,3,2] => 185 [7,3,1,1] => 185 [7,2,2,1] => 130 [7,2,1,1,1] => 95 [7,1,1,1,1,1] => 18 [6,6] => 109 [6,5,1] => 257 [6,4,2] => 163 [6,4,1,1] => 164 [6,3,3] => 72 [6,3,2,1] => 216 [6,3,1,1,1] => 76 [6,2,2,2] => 27 [6,2,2,1,1] => 78 [6,2,1,1,1,1] => 36 [6,1,1,1,1,1,1] => 8 [5,5,2] => 76 [5,5,1,1] => 78 [5,4,3] => 132 [5,4,2,1] => 196 [5,4,1,1,1] => 67 [5,3,3,1] => 87 [5,3,2,2] => 61 [5,3,2,1,1] => 132 [5,3,1,1,1,1] => 31 [5,2,2,2,1] => 32 [5,2,2,1,1,1] => 33 [5,2,1,1,1,1,1] => 12 [5,1,1,1,1,1,1,1] => 4 [4,4,4] => 20 [4,4,3,1] => 84 [4,4,2,2] => 31 [4,4,2,1,1] => 62 [4,4,1,1,1,1] => 14 [4,3,3,2] => 56 [4,3,3,1,1] => 55 [4,3,2,2,1] => 78 [4,3,2,1,1,1] => 57 [4,3,1,1,1,1,1] => 11 [4,2,2,2,2] => 5 [4,2,2,2,1,1] => 19 [4,2,2,1,1,1,1] => 13 [4,2,1,1,1,1,1,1] => 6 [4,1,1,1,1,1,1,1,1] => 2 [3,3,3,3] => 4 [3,3,3,2,1] => 24 [3,3,3,1,1,1] => 8 [3,3,2,2,2] => 9 [3,3,2,2,1,1] => 27 [3,3,2,1,1,1,1] => 13 [3,3,1,1,1,1,1,1] => 3 [3,2,2,2,2,1] => 7 [3,2,2,2,1,1,1] => 9 [3,2,2,1,1,1,1,1] => 5 [3,2,1,1,1,1,1,1,1] => 3 [3,1,1,1,1,1,1,1,1,1] => 1 [2,2,2,2,2,2] => 1 [2,2,2,2,2,1,1] => 1 [2,2,2,2,1,1,1,1] => 1 [2,2,2,1,1,1,1,1,1] => 1 [2,2,1,1,1,1,1,1,1,1] => 1 [2,1,1,1,1,1,1,1,1,1,1] => 1 [1,1,1,1,1,1,1,1,1,1,1,1] => 1 [13] => 1650 [12,1] => 1790 [11,2] => 1000 [11,1,1] => 1000 [10,3] => 730 [10,2,1] => 1098 [10,1,1,1] => 420 [9,4] => 601 [9,3,1] => 811 [9,2,2] => 308 [9,2,1,1] => 601 [9,1,1,1,1] => 150 [8,5] => 536 [8,4,1] => 675 [8,3,2] => 466 [8,3,1,1] => 466 [8,2,2,1] => 347 [8,2,1,1,1] => 263 [8,1,1,1,1,1] => 56 [7,6] => 513 [7,5,1] => 613 [7,4,2] => 399 [7,4,1,1] => 399 [7,3,3] => 180 [7,3,2,1] => 533 [7,3,1,1,1] => 200 [7,2,2,2] => 74 [7,2,2,1,1] => 194 [7,2,1,1,1,1] => 95 [7,1,1,1,1,1,1] => 18 [6,6,1] => 297 [6,5,2] => 365 [6,5,1,1] => 368 [6,4,3] => 308 [6,4,2,1] => 465 [6,4,1,1,1] => 179 [6,3,3,1] => 210 [6,3,2,2] => 156 [6,3,2,1,1] => 308 [6,3,1,1,1,1] => 76 [6,2,2,2,1] => 87 [6,2,2,1,1,1] => 82 [6,2,1,1,1,1,1] => 36 [6,1,1,1,1,1,1,1] => 8 [5,5,3] => 146 [5,5,2,1] => 222 [5,5,1,1,1] => 84 [5,4,4] => 137 [5,4,3,1] => 368 [5,4,2,2] => 142 [5,4,2,1,1] => 273 [5,4,1,1,1,1] => 67 [5,3,3,2] => 128 [5,3,3,1,1] => 125 [5,3,2,2,1] => 187 [5,3,2,1,1,1] => 140 [5,3,1,1,1,1,1] => 31 [5,2,2,2,2] => 14 [5,2,2,2,1,1] => 46 [5,2,2,1,1,1,1] => 33 [5,2,1,1,1,1,1,1] => 12 [5,1,1,1,1,1,1,1,1] => 4 [4,4,4,1] => 59 [4,4,3,2] => 120 [4,4,3,1,1] => 120 [4,4,2,2,1] => 90 [4,4,2,1,1,1] => 67 [4,4,1,1,1,1,1] => 14 [4,3,3,3] => 37 [4,3,3,2,1] => 161 [4,3,3,1,1,1] => 59 [4,3,2,2,2] => 43 [4,3,2,2,1,1] => 116 [4,3,2,1,1,1,1] => 57 [4,3,1,1,1,1,1,1] => 11 [4,2,2,2,2,1] => 17 [4,2,2,2,1,1,1] => 19 [4,2,2,1,1,1,1,1] => 13 [4,2,1,1,1,1,1,1,1] => 6 [4,1,1,1,1,1,1,1,1,1] => 2 [3,3,3,3,1] => 12 [3,3,3,2,2] => 18 [3,3,3,2,1,1] => 37 [3,3,3,1,1,1,1] => 8 [3,3,2,2,2,1] => 29 [3,3,2,2,1,1,1] => 27 [3,3,2,1,1,1,1,1] => 13 [3,3,1,1,1,1,1,1,1] => 3 [3,2,2,2,2,2] => 3 [3,2,2,2,2,1,1] => 10 [3,2,2,2,1,1,1,1] => 9 [3,2,2,1,1,1,1,1,1] => 5 [3,2,1,1,1,1,1,1,1,1] => 3 [3,1,1,1,1,1,1,1,1,1,1] => 1 [2,2,2,2,2,2,1] => 1 [2,2,2,2,2,1,1,1] => 1 [2,2,2,2,1,1,1,1,1] => 1 [2,2,2,1,1,1,1,1,1,1] => 1 [2,2,1,1,1,1,1,1,1,1,1] => 1 [2,1,1,1,1,1,1,1,1,1,1,1] => 1 [1,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [14] => 4973 [13,1] => 5346 [12,2] => 3126 [12,1,1] => 3126 [11,3] => 2140 [11,2,1] => 3402 [11,1,1,1] => 1296 [10,4] => 1753 [10,3,1] => 2354 [10,2,2] => 966 [10,2,1,1] => 1753 [10,1,1,1,1] => 420 [9,5] => 1548 [9,4,1] => 1944 [9,3,2] => 1386 [9,3,1,1] => 1386 [9,2,2,1] => 1080 [9,2,1,1,1] => 756 [9,1,1,1,1,1] => 150 [8,6] => 1452 [8,5,1] => 1743 [8,4,2] => 1179 [8,4,1,1] => 1179 [8,3,3] => 504 [8,3,2,1] => 1560 [8,3,1,1,1] => 594 [8,2,2,2] => 204 [8,2,2,1,1] => 576 [8,2,1,1,1,1] => 263 [8,1,1,1,1,1,1] => 56 [7,7] => 718 [7,6,1] => 1661 [7,5,2] => 1071 [7,5,1,1] => 1071 [7,4,3] => 844 [7,4,2,1] => 1350 [7,4,1,1,1] => 517 [7,3,3,1] => 577 [7,3,2,2] => 463 [7,3,2,1,1] => 844 [7,3,1,1,1,1] => 200 [7,2,2,2,1] => 229 [7,2,2,1,1,1] => 221 [7,2,1,1,1,1,1] => 95 [7,1,1,1,1,1,1,1] => 18 [6,6,2] => 507 [6,6,1,1] => 515 [6,5,3] => 783 [6,5,2,1] => 1244 [6,5,1,1,1] => 478 [6,4,4] => 371 [6,4,3,1] => 983 [6,4,2,2] => 412 [6,4,2,1,1] => 738 [6,4,1,1,1,1] => 179 [6,3,3,2] => 352 [6,3,3,1,1] => 346 [6,3,2,2,1] => 538 [6,3,2,1,1,1] => 380 [6,3,1,1,1,1,1] => 76 [6,2,2,2,2] => 37 [6,2,2,2,1,1] => 132 [6,2,2,1,1,1,1] => 82 [6,2,1,1,1,1,1,1] => 36 [6,1,1,1,1,1,1,1,1] => 8 [5,5,4] => 355 [5,5,3,1] => 470 [5,5,2,2] => 201 [5,5,2,1,1] => 355 [5,5,1,1,1,1] => 84 [5,4,4,1] => 440 [5,4,3,2] => 631 [5,4,3,1,1] => 631 [5,4,2,2,1] => 494 [5,4,2,1,1,1] => 344 [5,4,1,1,1,1,1] => 67 [5,3,3,3] => 92 [5,3,3,2,1] => 422 [5,3,3,1,1,1] => 156 [5,3,2,2,2] => 107 [5,3,2,2,1,1] => 309 [5,3,2,1,1,1,1] => 140 [5,3,1,1,1,1,1,1] => 31 [5,2,2,2,2,1] => 44 [5,2,2,2,1,1,1] => 50 [5,2,2,1,1,1,1,1] => 33 [5,2,1,1,1,1,1,1,1] => 12 [5,1,1,1,1,1,1,1,1,1] => 4 [4,4,4,2] => 103 [4,4,4,1,1] => 103 [4,4,3,3] => 128 [4,4,3,2,1] => 397 [4,4,3,1,1,1] => 153 [4,4,2,2,2] => 47 [4,4,2,2,1,1] => 151 [4,4,2,1,1,1,1] => 67 [4,4,1,1,1,1,1,1] => 14 [4,3,3,3,1] => 115 [4,3,3,2,2] => 136 [4,3,3,2,1,1] => 254 [4,3,3,1,1,1,1] => 59 [4,3,2,2,2,1] => 136 [4,3,2,2,1,1,1] => 130 [4,3,2,1,1,1,1,1] => 57 [4,3,1,1,1,1,1,1,1] => 11 [4,2,2,2,2,2] => 6 [4,2,2,2,2,1,1] => 23 [4,2,2,2,1,1,1,1] => 19 [4,2,2,1,1,1,1,1,1] => 13 [4,2,1,1,1,1,1,1,1,1] => 6 [4,1,1,1,1,1,1,1,1,1,1] => 2 [3,3,3,3,2] => 20 [3,3,3,3,1,1] => 20 [3,3,3,2,2,1] => 62 [3,3,3,2,1,1,1] => 40 [3,3,3,1,1,1,1,1] => 8 [3,3,2,2,2,2] => 13 [3,3,2,2,2,1,1] => 42 [3,3,2,2,1,1,1,1] => 27 [3,3,2,1,1,1,1,1,1] => 13 [3,3,1,1,1,1,1,1,1,1] => 3 [3,2,2,2,2,2,1] => 8 [3,2,2,2,2,1,1,1] => 10 [3,2,2,2,1,1,1,1,1] => 9 [3,2,2,1,1,1,1,1,1,1] => 5 [3,2,1,1,1,1,1,1,1,1,1] => 3 [3,1,1,1,1,1,1,1,1,1,1,1] => 1 [2,2,2,2,2,2,2] => 1 [2,2,2,2,2,2,1,1] => 1 [2,2,2,2,2,1,1,1,1] => 1 [2,2,2,2,1,1,1,1,1,1] => 1 [2,2,2,1,1,1,1,1,1,1,1] => 1 [2,2,1,1,1,1,1,1,1,1,1,1] => 1 [2,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [15] => 19522 [14,1] => 20919 [13,2] => 11264 [13,1,1] => 11264 [12,3] => 8450 [12,2,1] => 12204 [12,1,1,1] => 3786 [11,4] => 6656 [11,3,1] => 9216 [11,2,2] => 3328 [11,2,1,1] => 6656 [11,1,1,1,1] => 1350 [10,5] => 5837 [10,4,1] => 7322 [10,3,2] => 5069 [10,3,1,1] => 5069 [10,2,2,1] => 3661 [10,2,1,1,1] => 2253 [10,1,1,1,1,1] => 420 [9,6] => 5420 [9,5,1] => 6486 [9,4,2] => 4068 [9,4,1,1] => 4068 [9,3,3] => 1948 [9,3,2,1] => 5632 [9,3,1,1,1] => 1736 [9,2,2,2] => 682 [9,2,2,1,1] => 2034 [9,2,1,1,1,1] => 780 [9,1,1,1,1,1,1] => 150 [8,7] => 5232 [8,6,1] => 6096 [8,5,2] => 3648 [8,5,1,1] => 3648 [8,4,3] => 3168 [8,4,2,1] => 4576 [8,4,1,1,1] => 1428 [8,3,3,1] => 2192 [8,3,2,2] => 1584 [8,3,2,1,1] => 3168 [8,3,1,1,1,1] => 615 [8,2,2,2,1] => 768 [8,2,2,1,1,1] => 704 [8,2,1,1,1,1,1] => 263 [8,1,1,1,1,1,1,1] => 56 [7,7,1] => 2991 [7,6,2] => 3485 [7,6,1,1] => 3485 [7,5,3] => 2888 [7,5,2,1] => 4171 [7,5,1,1,1] => 1298 [7,4,4] => 1308 [7,4,3,1] => 3622 [7,4,2,2] => 1308 [7,4,2,1,1] => 2616 [7,4,1,1,1,1] => 538 [7,3,3,2] => 1253 [7,3,3,1,1] => 1253 [7,3,2,2,1] => 1811 [7,3,2,1,1,1] => 1116 [7,3,1,1,1,1,1] => 200 [7,2,2,2,2] => 112 [7,2,2,2,1,1] => 439 [7,2,2,1,1,1,1] => 225 [7,2,1,1,1,1,1,1] => 95 [7,1,1,1,1,1,1,1,1] => 18 [6,6,3] => 1405 [6,6,2,1] => 2030 [6,6,1,1,1] => 630 [6,5,4] => 2430 [6,5,3,1] => 3365 [6,5,2,2] => 1215 [6,5,2,1,1] => 2430 [6,5,1,1,1,1] => 498 [6,4,4,1] => 1524 [6,4,3,2] => 2110 [6,4,3,1,1] => 2110 [6,4,2,2,1] => 1524 [6,4,2,1,1,1] => 938 [6,4,1,1,1,1,1] => 179 [6,3,3,3] => 335 [6,3,3,2,1] => 1460 [6,3,3,1,1,1] => 450 [6,3,2,2,2] => 355 [6,3,2,2,1,1] => 1055 [6,3,2,1,1,1,1] => 390 [6,3,1,1,1,1,1,1] => 76 [6,2,2,2,2,1] => 131 [6,2,2,2,1,1,1] => 157 [6,2,2,1,1,1,1,1] => 82 [6,2,1,1,1,1,1,1,1] => 36 [6,1,1,1,1,1,1,1,1,1] => 8 [5,5,5] => 389 [5,5,4,1] => 1454 [5,5,3,2] => 1007 [5,5,3,1,1] => 1007 [5,5,2,2,1] => 727 [5,5,2,1,1,1] => 447 [5,5,1,1,1,1,1] => 84 [5,4,4,2] => 912 [5,4,4,1,1] => 912 [5,4,3,3] => 874 [5,4,3,2,1] => 2526 [5,4,3,1,1,1] => 778 [5,4,2,2,2] => 306 [5,4,2,2,1,1] => 912 [5,4,2,1,1,1,1] => 354 [5,4,1,1,1,1,1,1] => 67 [5,3,3,3,1] => 402 [5,3,3,2,2] => 437 [5,3,3,2,1,1] => 874 [5,3,3,1,1,1,1] => 160 [5,3,2,2,2,1] => 424 [5,3,2,2,1,1,1] => 389 [5,3,2,1,1,1,1,1] => 140 [5,3,1,1,1,1,1,1,1] => 31 [5,2,2,2,2,2] => 16 [5,2,2,2,2,1,1] => 78 [5,2,2,2,1,1,1,1] => 50 [5,2,2,1,1,1,1,1,1] => 33 [5,2,1,1,1,1,1,1,1,1] => 12 [5,1,1,1,1,1,1,1,1,1,1] => 4 [4,4,4,3] => 262 [4,4,4,2,1] => 380 [4,4,4,1,1,1] => 124 [4,4,3,3,1] => 548 [4,4,3,2,2] => 396 [4,4,3,2,1,1] => 792 [4,4,3,1,1,1,1] => 158 [4,4,2,2,2,1] => 192 [4,4,2,2,1,1,1] => 176 [4,4,2,1,1,1,1,1] => 67 [4,4,1,1,1,1,1,1,1] => 14 [4,3,3,3,2] => 252 [4,3,3,3,1,1] => 252 [4,3,3,2,2,1] => 548 [4,3,3,2,1,1,1] => 338 [4,3,3,1,1,1,1,1] => 59 [4,3,2,2,2,2] => 68 [4,3,2,2,2,1,1] => 266 [4,3,2,2,1,1,1,1] => 131 [4,3,2,1,1,1,1,1,1] => 57 [4,3,1,1,1,1,1,1,1,1] => 11 [4,2,2,2,2,2,1] => 20 [4,2,2,2,2,1,1,1] => 30 [4,2,2,2,1,1,1,1,1] => 19 [4,2,2,1,1,1,1,1,1,1] => 13 [4,2,1,1,1,1,1,1,1,1,1] => 6 [4,1,1,1,1,1,1,1,1,1,1,1] => 2 [3,3,3,3,3] => 12 [3,3,3,3,2,1] => 87 [3,3,3,3,1,1,1] => 26 [3,3,3,2,2,2] => 43 [3,3,3,2,2,1,1] => 126 [3,3,3,2,1,1,1,1] => 40 [3,3,3,1,1,1,1,1,1] => 8 [3,3,2,2,2,2,1] => 47 [3,3,2,2,2,1,1,1] => 57 [3,3,2,2,1,1,1,1,1] => 27 [3,3,2,1,1,1,1,1,1,1] => 13 [3,3,1,1,1,1,1,1,1,1,1] => 3 [3,2,2,2,2,2,2] => 3 [3,2,2,2,2,2,1,1] => 14 [3,2,2,2,2,1,1,1,1] => 10 [3,2,2,2,1,1,1,1,1,1] => 9 [3,2,2,1,1,1,1,1,1,1,1] => 5 [3,2,1,1,1,1,1,1,1,1,1,1] => 3 [3,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [2,2,2,2,2,2,2,1] => 1 [2,2,2,2,2,2,1,1,1] => 1 [2,2,2,2,2,1,1,1,1,1] => 1 [2,2,2,2,1,1,1,1,1,1,1] => 1 [2,2,2,1,1,1,1,1,1,1,1,1] => 1 [2,2,1,1,1,1,1,1,1,1,1,1,1] => 1 [2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [16] => 72072 [15,1] => 76877 [14,2] => 42900 [14,1,1] => 42900 [13,3] => 30228 [13,2,1] => 46200 [13,1,1,1] => 15972 [12,4] => 24069 [12,3,1] => 32748 [12,2,2] => 12903 [12,2,1,1] => 24069 [12,1,1,1,1] => 4224 [11,5] => 20937 [11,4,1] => 26256 [11,3,2] => 18627 [11,3,1,1] => 18627 [11,2,2,1] => 14076 [11,2,1,1,1] => 9159 [11,1,1,1,1,1] => 1350 [10,6] => 19224 [10,5,1] => 23031 [10,4,2] => 15038 [10,4,1,1] => 15038 [10,3,3] => 6691 [10,3,2,1] => 20490 [10,3,1,1,1] => 7108 [10,2,2,2] => 2645 [10,2,2,1,1] => 7459 [10,2,1,1,1,1] => 2496 [10,1,1,1,1,1,1] => 420 [9,7] => 18306 [9,6,1] => 21360 [9,5,2] => 13326 [9,5,1,1] => 13326 [9,4,3] => 10936 [9,4,2,1] => 16709 [9,4,1,1,1] => 5773 [9,3,3,1] => 7434 [9,3,2,2] => 5874 [9,3,2,1,1] => 10936 [9,3,1,1,1,1] => 1942 [9,2,2,2,1] => 2939 [9,2,2,1,1,1] => 2711 [9,2,1,1,1,1,1] => 780 [9,1,1,1,1,1,1,1] => 150 [8,8] => 9010 [8,7,1] => 20595 [8,6,2] => 12515 [8,6,1,1] => 12515 [8,5,3] => 9812 [8,5,2,1] => 14992 [8,5,1,1,1] => 5180 [8,4,4] => 4521 [8,4,3,1] => 12304 [8,4,2,2] => 4846 [8,4,2,1,1] => 9042 [8,4,1,1,1,1] => 1584 [8,3,3,2] => 4366 [8,3,3,1,1] => 4366 [8,3,2,2,1] => 6608 [8,3,2,1,1,1] => 4308 [8,3,1,1,1,1,1] => 615 [8,2,2,2,2] => 419 [8,2,2,2,1,1] => 1594 [8,2,2,1,1,1,1] => 768 [8,2,1,1,1,1,1,1] => 263 [8,1,1,1,1,1,1,1,1] => 56 [7,7,2] => 6130 [7,7,1,1] => 6130 [7,6,3] => 9359 [7,6,2,1] => 14304 [7,6,1,1,1] => 4945 [7,5,4] => 8241 [7,5,3,1] => 11214 [7,5,2,2] => 4417 [7,5,2,1,1] => 8241 [7,5,1,1,1,1] => 1444 [7,4,4,1] => 5167 [7,4,3,2] => 7330 [7,4,3,1,1] => 7330 [7,4,2,2,1] => 5539 [7,4,2,1,1,1] => 3602 [7,4,1,1,1,1,1] => 538 [7,3,3,3] => 1084 [7,3,3,2,1] => 4990 [7,3,3,1,1,1] => 1737 [7,3,2,2,2] => 1291 [7,3,2,2,1,1] => 3635 [7,3,2,1,1,1,1] => 1229 [7,3,1,1,1,1,1,1] => 200 [7,2,2,2,2,1] => 479 [7,2,2,2,1,1,1] => 561 [7,2,2,1,1,1,1,1] => 225 [7,2,1,1,1,1,1,1,1] => 95 [7,1,1,1,1,1,1,1,1,1] => 18 [6,6,4] => 4013 [6,6,3,1] => 5460 [6,6,2,2] => 2151 [6,6,2,1,1] => 4013 [6,6,1,1,1,1] => 704 [6,5,5] => 3834 [6,5,4,1] => 9616 [6,5,3,2] => 6821 [6,5,3,1,1] => 6821 [6,5,2,2,1] => 5153 [6,5,2,1,1,1] => 3352 [6,5,1,1,1,1,1] => 498 [6,4,4,2] => 3138 [6,4,4,1,1] => 3138 [6,4,3,3] => 2794 [6,4,3,2,1] => 8552 [6,4,3,1,1,1] => 2964 [6,4,2,2,2] => 1104 [6,4,2,2,1,1] => 3114 [6,4,2,1,1,1,1] => 1040 [6,4,1,1,1,1,1,1] => 179 [6,3,3,3,1] => 1265 [6,3,3,2,2] => 1503 [6,3,3,2,1,1] => 2794 [6,3,3,1,1,1,1] => 501 [6,3,2,2,2,1] => 1506 [6,3,2,2,1,1,1] => 1390 [6,3,2,1,1,1,1,1] => 390 [6,3,1,1,1,1,1,1,1] => 76 [6,2,2,2,2,2] => 56 [6,2,2,2,2,1,1] => 269 [6,2,2,2,1,1,1,1] => 168 [6,2,2,1,1,1,1,1,1] => 82 [6,2,1,1,1,1,1,1,1,1] => 36 [6,1,1,1,1,1,1,1,1,1,1] => 8 [5,5,5,1] => 1531 [5,5,4,2] => 2998 [5,5,4,1,1] => 2998 [5,5,3,3] => 1335 [5,5,3,2,1] => 4086 [5,5,3,1,1,1] => 1416 [5,5,2,2,2] => 527 [5,5,2,2,1,1] => 1487 [5,5,2,1,1,1,1] => 496 [5,5,1,1,1,1,1,1] => 84 [5,4,4,3] => 2462 [5,4,4,2,1] => 3759 [5,4,4,1,1,1] => 1297 [5,4,3,3,1] => 3348 [5,4,3,2,2] => 2643 [5,4,3,2,1,1] => 4924 [5,4,3,1,1,1,1] => 871 [5,4,2,2,2,1] => 1322 [5,4,2,2,1,1,1] => 1219 [5,4,2,1,1,1,1,1] => 354 [5,4,1,1,1,1,1,1,1] => 67 [5,3,3,3,2] => 792 [5,3,3,3,1,1] => 792 [5,3,3,2,2,1] => 1801 [5,3,3,2,1,1,1] => 1176 [5,3,3,1,1,1,1,1] => 160 [5,3,2,2,2,2] => 229 [5,3,2,2,2,1,1] => 869 [5,3,2,2,1,1,1,1] => 422 [5,3,2,1,1,1,1,1,1] => 140 [5,3,1,1,1,1,1,1,1,1] => 31 [5,2,2,2,2,2,1] => 67 [5,2,2,2,2,1,1,1] => 94 [5,2,2,2,1,1,1,1,1] => 50 [5,2,2,1,1,1,1,1,1,1] => 33 [5,2,1,1,1,1,1,1,1,1,1] => 12 [5,1,1,1,1,1,1,1,1,1,1,1] => 4 [4,4,4,4] => 188 [4,4,4,3,1] => 1028 [4,4,4,2,2] => 405 [4,4,4,2,1,1] => 755 [4,4,4,1,1,1,1] => 132 [4,4,3,3,2] => 1095 [4,4,3,3,1,1] => 1095 [4,4,3,2,2,1] => 1657 [4,4,3,2,1,1,1] => 1079 [4,4,3,1,1,1,1,1] => 158 [4,4,2,2,2,2] => 105 [4,4,2,2,2,1,1] => 400 [4,4,2,2,1,1,1,1] => 192 [4,4,2,1,1,1,1,1,1] => 67 [4,4,1,1,1,1,1,1,1,1] => 14 [4,3,3,3,3] => 162 [4,3,3,3,2,1] => 993 [4,3,3,3,1,1,1] => 346 [4,3,3,2,2,2] => 386 [4,3,3,2,2,1,1] => 1086 [4,3,3,2,1,1,1,1] => 370 [4,3,3,1,1,1,1,1,1] => 59 [4,3,2,2,2,2,1] => 287 [4,3,2,2,2,1,1,1] => 336 [4,3,2,2,1,1,1,1,1] => 131 [4,3,2,1,1,1,1,1,1,1] => 57 [4,3,1,1,1,1,1,1,1,1,1] => 11 [4,2,2,2,2,2,2] => 7 [4,2,2,2,2,2,1,1] => 40 [4,2,2,2,2,1,1,1,1] => 31 [4,2,2,2,1,1,1,1,1,1] => 19 [4,2,2,1,1,1,1,1,1,1,1] => 13 [4,2,1,1,1,1,1,1,1,1,1,1] => 6 [4,1,1,1,1,1,1,1,1,1,1,1,1] => 2 [3,3,3,3,3,1] => 44 [3,3,3,3,2,2] => 87 [3,3,3,3,2,1,1] => 162 [3,3,3,3,1,1,1,1] => 29 [3,3,3,2,2,2,1] => 175 [3,3,3,2,2,1,1,1] => 162 [3,3,3,2,1,1,1,1,1] => 40 [3,3,3,1,1,1,1,1,1,1] => 8 [3,3,2,2,2,2,2] => 20 [3,3,2,2,2,2,1,1] => 94 [3,3,2,2,2,1,1,1,1] => 60 [3,3,2,2,1,1,1,1,1,1] => 27 [3,3,2,1,1,1,1,1,1,1,1] => 13 [3,3,1,1,1,1,1,1,1,1,1,1] => 3 [3,2,2,2,2,2,2,1] => 10 [3,2,2,2,2,2,1,1,1] => 15 [3,2,2,2,2,1,1,1,1,1] => 10 [3,2,2,2,1,1,1,1,1,1,1] => 9 [3,2,2,1,1,1,1,1,1,1,1,1] => 5 [3,2,1,1,1,1,1,1,1,1,1,1,1] => 3 [3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [2,2,2,2,2,2,2,2] => 1 [2,2,2,2,2,2,2,1,1] => 1 [2,2,2,2,2,2,1,1,1,1] => 1 [2,2,2,2,2,1,1,1,1,1,1] => 1 [2,2,2,2,1,1,1,1,1,1,1,1] => 1 [2,2,2,1,1,1,1,1,1,1,1,1,1] => 1 [2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 1 [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1 ----------------------------------------------------------------------------- Created: May 25, 2023 at 14:39 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: May 25, 2023 at 14:39 by Martin Rubey