***************************************************************************** * 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: St000934 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The 2-degree of an integer partition. For an integer partition $\lambda$, this is given by the exponent of 2 in the Gram determinant of the integal Specht module of the symmetric group indexed by $\lambda$. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(L): return L.prime_degree(2) ----------------------------------------------------------------------------- Statistic values: [2] => 1 [1,1] => 0 [3] => 1 [2,1] => 0 [1,1,1] => 0 [4] => 2 [3,1] => 5 [2,2] => 2 [2,1,1] => 1 [1,1,1,1] => 0 [5] => 3 [4,1] => 4 [3,2] => 14 [3,1,1] => 6 [2,2,1] => 1 [2,1,1,1] => 0 [1,1,1,1,1] => 0 [6] => 4 [5,1] => 19 [4,2] => 27 [4,1,1] => 16 [3,3] => 14 [3,2,1] => 0 [3,1,1,1] => 14 [2,2,2] => 6 [2,2,1,1] => 9 [2,1,1,1,1] => 1 [1,1,1,1,1,1] => 0 [7] => 4 [6,1] => 18 [5,2] => 42 [5,1,1] => 45 [4,3] => 36 [4,2,1] => 97 [4,1,1,1] => 20 [3,3,1] => 62 [3,2,2] => 22 [3,2,1,1] => 43 [3,1,1,1,1] => 15 [2,2,2,1] => 6 [2,2,1,1,1] => 0 [2,1,1,1,1,1] => 0 [1,1,1,1,1,1,1] => 0 [8] => 6 [7,1] => 40 [6,2] => 94 [6,1,1] => 93 [5,3] => 106 [5,2,1] => 64 [5,1,1,1] => 145 [4,4] => 64 [4,3,1] => 342 [4,2,2] => 154 [4,2,1,1] => 270 [4,1,1,1,1] => 65 [3,3,2] => 126 [3,3,1,1] => 70 [3,2,2,1] => 78 [3,2,1,1,1] => 0 [3,1,1,1,1,1] => 33 [2,2,2,2] => 20 [2,2,2,1,1] => 34 [2,2,1,1,1,1] => 6 [2,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1] => 0 [9] => 7 [8,1] => 32 [7,2] => 187 [7,1,1] => 112 [6,3] => 144 [6,2,1] => 629 [6,1,1,1] => 168 [5,4] => 226 [5,3,1] => 704 [5,2,2] => 282 [5,2,1,1] => 659 [5,1,1,1,1] => 210 [4,4,1] => 266 [4,3,2] => 664 [4,3,1,1] => 592 [4,2,2,1] => 272 [4,2,1,1,1] => 664 [4,1,1,1,1,1] => 56 [3,3,3] => 126 [3,3,2,1] => 8 [3,3,1,1,1] => 198 [3,2,2,2] => 154 [3,2,2,1,1] => 268 [3,2,1,1,1,1] => 106 [3,1,1,1,1,1,1] => 28 [2,2,2,2,1] => 26 [2,2,2,1,1,1] => 0 [2,2,1,1,1,1,1] => 2 [2,1,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1,1] => 0 [10] => 8 [9,1] => 71 [8,2] => 254 [8,1,1] => 172 [7,3] => 571 [7,2,1] => 480 [7,1,1,1] => 392 [6,4] => 508 [6,3,1] => 2116 [6,2,2] => 1496 [6,2,1,1] => 1568 [6,1,1,1,1] => 448 [5,5] => 226 [5,4,1] => 704 [5,3,2] => 2436 [5,3,1,1] => 2630 [5,2,2,1] => 1888 [5,2,1,1,1] => 448 [5,1,1,1,1,1] => 434 [4,4,2] => 1182 [4,4,1,1] => 1074 [4,3,3] => 832 [4,3,2,1] => 0 [4,3,1,1,1] => 2312 [4,2,2,2] => 726 [4,2,2,1,1] => 1906 [4,2,1,1,1,1] => 882 [4,1,1,1,1,1,1] => 112 [3,3,3,1] => 638 [3,3,2,2] => 330 [3,3,2,1,1] => 714 [3,3,1,1,1,1] => 304 [3,2,2,2,1] => 160 [3,2,2,1,1,1] => 404 [3,2,1,1,1,1,1] => 0 [3,1,1,1,1,1,1,1] => 44 [2,2,2,2,2] => 68 [2,2,2,2,1,1] => 122 [2,2,2,1,1,1,1] => 29 [2,2,1,1,1,1,1,1] => 26 [2,1,1,1,1,1,1,1,1] => 1 [1,1,1,1,1,1,1,1,1,1] => 0 [11] => 8 [10,1] => 70 [9,2] => 264 [9,1,1] => 315 [8,3] => 750 [8,2,1] => 1670 [8,1,1,1] => 480 [7,4] => 1319 [7,3,1] => 3332 [7,2,2] => 2136 [7,2,1,1] => 2608 [7,1,1,1,1] => 840 [6,5] => 692 [6,4,1] => 4138 [6,3,2] => 6588 [6,3,1,1] => 3696 [6,2,2,1] => 3552 [6,2,1,1,1] => 4004 [6,1,1,1,1,1] => 756 [5,5,1] => 1794 [5,4,2] => 5312 [5,4,1,1] => 5575 [5,3,3] => 3058 [5,3,2,1] => 10188 [5,3,1,1,1] => 5236 [5,2,2,2] => 3739 [5,2,2,1,1] => 4004 [5,2,1,1,1,1] => 1540 [5,1,1,1,1,1,1] => 630 [4,4,3] => 1804 [4,4,2,1] => 5028 [4,4,1,1,1] => 2861 [4,3,3,1] => 3564 [4,3,2,2] => 1572 [4,3,2,1,1] => 5982 [4,3,1,1,1,1] => 3048 [4,2,2,2,1] => 3665 [4,2,2,1,1,1] => 1232 [4,2,1,1,1,1,1] => 1550 [4,1,1,1,1,1,1,1] => 120 [3,3,3,2] => 1430 [3,3,3,1,1] => 902 [3,3,2,2,1] => 1618 [3,3,2,1,1,1] => 342 [3,3,1,1,1,1,1] => 944 [3,2,2,2,2] => 516 [3,2,2,2,1,1] => 1406 [3,2,2,1,1,1,1] => 518 [3,2,1,1,1,1,1,1] => 178 [3,1,1,1,1,1,1,1,1] => 45 [2,2,2,2,2,1] => 100 [2,2,2,2,1,1,1] => 1 [2,2,2,1,1,1,1,1] => 20 [2,2,1,1,1,1,1,1,1] => 0 [2,1,1,1,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1,1,1,1] => 0 [12] => 10 [11,1] => 108 [10,2] => 476 [10,1,1] => 475 [9,3] => 1234 [9,2,1] => 1280 [9,1,1,1] => 1395 [8,4] => 2619 [8,3,1] => 8095 [8,2,2] => 3652 [8,2,1,1] => 6780 [8,1,1,1,1] => 1740 [7,5] => 2539 [7,4,1] => 4224 [7,3,2] => 15961 [7,3,1,1] => 12738 [7,2,2,1] => 12102 [7,2,1,1,1] => 5184 [7,1,1,1,1,1] => 2352 [6,6] => 824 [6,5,1] => 9693 [6,4,2] => 20691 [6,4,1,1] => 13486 [6,3,3] => 11626 [6,3,2,1] => 5632 [6,3,1,1,1] => 14784 [6,2,2,2] => 10041 [6,2,2,1,1] => 16488 [6,2,1,1,1,1] => 8400 [6,1,1,1,1,1,1] => 1806 [5,5,2] => 6446 [5,5,1,1] => 8524 [5,4,3] => 8128 [5,4,2,1] => 40788 [5,4,1,1,1] => 8832 [5,3,3,1] => 27304 [5,3,2,2] => 24409 [5,3,2,1,1] => 30800 [5,3,1,1,1,1] => 12024 [5,2,2,2,1] => 5248 [5,2,2,1,1,1] => 7392 [5,2,1,1,1,1,1] => 1728 [5,1,1,1,1,1,1,1] => 1230 [4,4,4] => 2728 [4,4,3,1] => 16732 [4,4,2,2] => 7920 [4,4,2,1,1] => 20141 [4,4,1,1,1,1] => 9209 [4,3,3,2] => 9998 [4,3,3,1,1] => 10118 [4,3,2,2,1] => 16962 [4,3,2,1,1,1] => 0 [4,3,1,1,1,1,1] => 8688 [4,2,2,2,2] => 6326 [4,2,2,2,1,1] => 8074 [4,2,2,1,1,1,1] => 3894 [4,2,1,1,1,1,1,1] => 2670 [4,1,1,1,1,1,1,1,1] => 255 [3,3,3,3] => 1430 [3,3,3,2,1] => 320 [3,3,3,1,1,1] => 3224 [3,3,2,2,2] => 2794 [3,3,2,2,1,1] => 6039 [3,3,2,1,1,1,1] => 3289 [3,3,1,1,1,1,1,1] => 660 [3,2,2,2,2,1] => 1857 [3,2,2,2,1,1,1] => 0 [3,2,2,1,1,1,1,1] => 815 [3,2,1,1,1,1,1,1,1] => 0 [3,1,1,1,1,1,1,1,1,1] => 75 [2,2,2,2,2,2] => 232 [2,2,2,2,2,1,1] => 431 [2,2,2,2,1,1,1,1] => 131 [2,2,2,1,1,1,1,1,1] => 152 [2,2,1,1,1,1,1,1,1,1] => 10 [2,1,1,1,1,1,1,1,1,1,1] => 2 [1,1,1,1,1,1,1,1,1,1,1,1] => 0 ----------------------------------------------------------------------------- Created: Aug 11, 2017 at 17:05 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Aug 11, 2017 at 17:05 by Christian Stump