***************************************************************************** * 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: St001547 ----------------------------------------------------------------------------- Collection: Decorated permutations ----------------------------------------------------------------------------- Description: The sum of all indices from every element of the Grassmann necklace. Here, we use Postnikov's map (p.59) from decorated permutations to Grassmann necklaces. ----------------------------------------------------------------------------- References: [1] A. Postnikov, ''Total positivity, Grassmannians, and networks.'' 27 Sep 2006. Postnikov, A. Total positivity, Grassmannians, and networks [[arXiv:math/0609764]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [+,+] => 0 [-,+] => 2 [+,-] => 4 [-,-] => 6 [2,1] => 3 [+,+,+] => 0 [-,+,+] => 3 [+,-,+] => 6 [+,+,-] => 9 [-,-,+] => 9 [-,+,-] => 12 [+,-,-] => 15 [-,-,-] => 18 [+,3,2] => 7 [-,3,2] => 10 [2,1,+] => 4 [2,1,-] => 13 [2,3,1] => 6 [3,1,2] => 12 [3,+,1] => 7 [3,-,1] => 13 [+,+,+,+] => 0 [-,+,+,+] => 4 [+,-,+,+] => 8 [+,+,-,+] => 12 [+,+,+,-] => 16 [-,-,+,+] => 12 [-,+,-,+] => 16 [-,+,+,-] => 20 [+,-,-,+] => 20 [+,-,+,-] => 24 [+,+,-,-] => 28 [-,-,-,+] => 24 [-,-,+,-] => 28 [-,+,-,-] => 32 [+,-,-,-] => 36 [-,-,-,-] => 40 [+,+,4,3] => 13 [-,+,4,3] => 17 [+,-,4,3] => 21 [-,-,4,3] => 25 [+,3,2,+] => 9 [-,3,2,+] => 13 [+,3,2,-] => 25 [-,3,2,-] => 29 [+,3,4,2] => 11 [-,3,4,2] => 15 [+,4,2,3] => 23 [-,4,2,3] => 27 [+,4,+,2] => 12 [-,4,+,2] => 16 [+,4,-,2] => 24 [-,4,-,2] => 28 [2,1,+,+] => 5 [2,1,-,+] => 17 [2,1,+,-] => 21 [2,1,-,-] => 33 [2,1,4,3] => 18 [2,3,1,+] => 7 [2,3,1,-] => 23 [2,3,4,1] => 10 [2,4,1,3] => 21 [2,4,+,1] => 11 [2,4,-,1] => 23 [3,1,2,+] => 15 [3,1,2,-] => 31 [3,1,4,2] => 17 [3,+,1,+] => 8 [3,-,1,+] => 16 [3,+,1,-] => 24 [3,-,1,-] => 32 [3,+,4,1] => 11 [3,-,4,1] => 19 [3,4,1,2] => 20 [3,4,2,1] => 21 [4,1,2,3] => 30 [4,1,+,2] => 19 [4,1,-,2] => 31 [4,+,1,3] => 23 [4,-,1,3] => 31 [4,+,+,1] => 13 [4,-,+,1] => 21 [4,+,-,1] => 25 [4,-,-,1] => 33 [4,3,1,2] => 21 [4,3,2,1] => 22 [+,+,+,+,+] => 0 [-,+,+,+,+] => 5 [+,-,+,+,+] => 10 [+,+,-,+,+] => 15 [+,+,+,-,+] => 20 [+,+,+,+,-] => 25 [-,-,+,+,+] => 15 [-,+,-,+,+] => 20 [-,+,+,-,+] => 25 [-,+,+,+,-] => 30 [+,-,-,+,+] => 25 [+,-,+,-,+] => 30 [+,-,+,+,-] => 35 [+,+,-,-,+] => 35 [+,+,-,+,-] => 40 [+,+,+,-,-] => 45 [-,-,-,+,+] => 30 [-,-,+,-,+] => 35 [-,-,+,+,-] => 40 [-,+,-,-,+] => 40 [-,+,-,+,-] => 45 [-,+,+,-,-] => 50 [+,-,-,-,+] => 45 [+,-,-,+,-] => 50 [+,-,+,-,-] => 55 [+,+,-,-,-] => 60 [-,-,-,-,+] => 50 [-,-,-,+,-] => 55 [-,-,+,-,-] => 60 [-,+,-,-,-] => 65 [+,-,-,-,-] => 70 [-,-,-,-,-] => 75 [+,+,+,5,4] => 21 [-,+,+,5,4] => 26 [+,-,+,5,4] => 31 [+,+,-,5,4] => 36 [-,-,+,5,4] => 36 [-,+,-,5,4] => 41 [+,-,-,5,4] => 46 [-,-,-,5,4] => 51 [+,+,4,3,+] => 16 [-,+,4,3,+] => 21 [+,-,4,3,+] => 26 [+,+,4,3,-] => 41 [-,-,4,3,+] => 31 [-,+,4,3,-] => 46 [+,-,4,3,-] => 51 [-,-,4,3,-] => 56 [+,+,4,5,3] => 18 [-,+,4,5,3] => 23 [+,-,4,5,3] => 28 [-,-,4,5,3] => 33 [+,+,5,3,4] => 38 [-,+,5,3,4] => 43 [+,-,5,3,4] => 48 [-,-,5,3,4] => 53 [+,+,5,+,3] => 19 [-,+,5,+,3] => 24 [+,-,5,+,3] => 29 [+,+,5,-,3] => 39 [-,-,5,+,3] => 34 [-,+,5,-,3] => 44 [+,-,5,-,3] => 49 [-,-,5,-,3] => 54 [+,3,2,+,+] => 11 [-,3,2,+,+] => 16 [+,3,2,-,+] => 31 [+,3,2,+,-] => 36 [-,3,2,-,+] => 36 [-,3,2,+,-] => 41 [+,3,2,-,-] => 56 [-,3,2,-,-] => 61 [+,3,2,5,4] => 32 [-,3,2,5,4] => 37 [+,3,4,2,+] => 13 [-,3,4,2,+] => 18 [+,3,4,2,-] => 38 [-,3,4,2,-] => 43 [+,3,4,5,2] => 16 [-,3,4,5,2] => 21 [+,3,5,2,4] => 35 [-,3,5,2,4] => 40 [+,3,5,+,2] => 17 [-,3,5,+,2] => 22 [+,3,5,-,2] => 37 [-,3,5,-,2] => 42 [+,4,2,3,+] => 28 [-,4,2,3,+] => 33 [+,4,2,3,-] => 53 [-,4,2,3,-] => 58 [+,4,2,5,3] => 30 [-,4,2,5,3] => 35 [+,4,+,2,+] => 14 [-,4,+,2,+] => 19 [+,4,-,2,+] => 29 [+,4,+,2,-] => 39 [-,4,-,2,+] => 34 [-,4,+,2,-] => 44 [+,4,-,2,-] => 54 [-,4,-,2,-] => 59 [+,4,+,5,2] => 17 [-,4,+,5,2] => 22 [+,4,-,5,2] => 32 [-,4,-,5,2] => 37 [+,4,5,2,3] => 33 [-,4,5,2,3] => 38 [+,4,5,3,2] => 34 [-,4,5,3,2] => 39 [+,5,2,3,4] => 51 [-,5,2,3,4] => 56 [+,5,2,+,3] => 32 [-,5,2,+,3] => 37 [+,5,2,-,3] => 52 [-,5,2,-,3] => 57 [+,5,+,2,4] => 37 [-,5,+,2,4] => 42 [+,5,-,2,4] => 52 [-,5,-,2,4] => 57 [+,5,+,+,2] => 19 [-,5,+,+,2] => 24 [+,5,-,+,2] => 34 [+,5,+,-,2] => 39 [-,5,-,+,2] => 39 [-,5,+,-,2] => 44 [+,5,-,-,2] => 54 [-,5,-,-,2] => 59 [+,5,4,2,3] => 34 [-,5,4,2,3] => 39 [+,5,4,3,2] => 35 [-,5,4,3,2] => 40 [2,1,+,+,+] => 6 [2,1,-,+,+] => 21 [2,1,+,-,+] => 26 [2,1,+,+,-] => 31 [2,1,-,-,+] => 41 [2,1,-,+,-] => 46 [2,1,+,-,-] => 51 [2,1,-,-,-] => 66 [2,1,+,5,4] => 27 [2,1,-,5,4] => 42 [2,1,4,3,+] => 22 [2,1,4,3,-] => 47 [2,1,4,5,3] => 24 [2,1,5,3,4] => 44 [2,1,5,+,3] => 25 [2,1,5,-,3] => 45 [2,3,1,+,+] => 8 [2,3,1,-,+] => 28 [2,3,1,+,-] => 33 [2,3,1,-,-] => 53 [2,3,1,5,4] => 29 [2,3,4,1,+] => 11 [2,3,4,1,-] => 36 [2,3,4,5,1] => 15 [2,3,5,1,4] => 33 [2,3,5,+,1] => 16 [2,3,5,-,1] => 36 [2,4,1,3,+] => 25 [2,4,1,3,-] => 50 [2,4,1,5,3] => 27 [2,4,+,1,+] => 12 [2,4,-,1,+] => 27 [2,4,+,1,-] => 37 [2,4,-,1,-] => 52 [2,4,+,5,1] => 16 [2,4,-,5,1] => 31 [2,4,5,1,3] => 31 [2,4,5,3,1] => 33 [2,5,1,3,4] => 48 [2,5,1,+,3] => 29 [2,5,1,-,3] => 49 [2,5,+,1,4] => 35 [2,5,-,1,4] => 50 [2,5,+,+,1] => 18 [2,5,-,+,1] => 33 [2,5,+,-,1] => 38 [2,5,-,-,1] => 53 [2,5,4,1,3] => 32 [2,5,4,3,1] => 34 [3,1,2,+,+] => 18 [3,1,2,-,+] => 38 [3,1,2,+,-] => 43 [3,1,2,-,-] => 63 [3,1,2,5,4] => 39 [3,1,4,2,+] => 20 [3,1,4,2,-] => 45 [3,1,4,5,2] => 23 [3,1,5,2,4] => 42 [3,1,5,+,2] => 24 [3,1,5,-,2] => 44 [3,+,1,+,+] => 9 [3,-,1,+,+] => 19 [3,+,1,-,+] => 29 [3,+,1,+,-] => 34 [3,-,1,-,+] => 39 [3,-,1,+,-] => 44 [3,+,1,-,-] => 54 [3,-,1,-,-] => 64 [3,+,1,5,4] => 30 [3,-,1,5,4] => 40 [3,+,4,1,+] => 12 [3,-,4,1,+] => 22 [3,+,4,1,-] => 37 [3,-,4,1,-] => 47 [3,+,4,5,1] => 16 [3,-,4,5,1] => 26 [3,+,5,1,4] => 34 [3,-,5,1,4] => 44 [3,+,5,+,1] => 17 [3,-,5,+,1] => 27 [3,+,5,-,1] => 37 [3,-,5,-,1] => 47 [3,4,1,2,+] => 23 [3,4,1,2,-] => 48 [3,4,1,5,2] => 26 [3,4,2,1,+] => 24 [3,4,2,1,-] => 49 [3,4,2,5,1] => 28 [3,4,5,1,2] => 30 [3,4,5,2,1] => 31 [3,5,1,2,4] => 46 [3,5,1,+,2] => 28 [3,5,1,-,2] => 48 [3,5,2,1,4] => 47 [3,5,2,+,1] => 30 [3,5,2,-,1] => 50 [3,5,4,1,2] => 31 [3,5,4,2,1] => 32 [4,1,2,3,+] => 36 [4,1,2,3,-] => 61 [4,1,2,5,3] => 38 [4,1,+,2,+] => 22 [4,1,-,2,+] => 37 [4,1,+,2,-] => 47 [4,1,-,2,-] => 62 [4,1,+,5,2] => 25 [4,1,-,5,2] => 40 [4,1,5,2,3] => 41 [4,1,5,3,2] => 42 [4,+,1,3,+] => 27 [4,-,1,3,+] => 37 [4,+,1,3,-] => 52 [4,-,1,3,-] => 62 [4,+,1,5,3] => 29 [4,-,1,5,3] => 39 [4,+,+,1,+] => 14 [4,-,+,1,+] => 24 [4,+,-,1,+] => 29 [4,+,+,1,-] => 39 [4,-,-,1,+] => 39 [4,-,+,1,-] => 49 [4,+,-,1,-] => 54 [4,-,-,1,-] => 64 [4,+,+,5,1] => 18 [4,-,+,5,1] => 28 [4,+,-,5,1] => 33 [4,-,-,5,1] => 43 [4,+,5,1,3] => 33 [4,-,5,1,3] => 43 [4,+,5,3,1] => 35 [4,-,5,3,1] => 45 [4,3,1,2,+] => 24 [4,3,1,2,-] => 49 [4,3,1,5,2] => 27 [4,3,2,1,+] => 25 [4,3,2,1,-] => 50 [4,3,2,5,1] => 29 [4,3,5,1,2] => 31 [4,3,5,2,1] => 32 [4,5,1,2,3] => 45 [4,5,1,3,2] => 46 [4,5,2,1,3] => 46 [4,5,2,3,1] => 48 [4,5,+,1,2] => 33 [4,5,-,1,2] => 48 [4,5,+,2,1] => 34 [4,5,-,2,1] => 49 [5,1,2,3,4] => 60 [5,1,2,+,3] => 41 [5,1,2,-,3] => 61 [5,1,+,2,4] => 46 [5,1,-,2,4] => 61 [5,1,+,+,2] => 28 [5,1,-,+,2] => 43 [5,1,+,-,2] => 48 [5,1,-,-,2] => 63 [5,1,4,2,3] => 43 [5,1,4,3,2] => 44 [5,+,1,3,4] => 51 [5,-,1,3,4] => 61 [5,+,1,+,3] => 32 [5,-,1,+,3] => 42 [5,+,1,-,3] => 52 [5,-,1,-,3] => 62 [5,+,+,1,4] => 38 [5,-,+,1,4] => 48 [5,+,-,1,4] => 53 [5,-,-,1,4] => 63 [5,+,+,+,1] => 21 [5,-,+,+,1] => 31 [5,+,-,+,1] => 36 [5,+,+,-,1] => 41 [5,-,-,+,1] => 46 [5,-,+,-,1] => 51 [5,+,-,-,1] => 56 [5,-,-,-,1] => 66 [5,+,4,1,3] => 35 [5,-,4,1,3] => 45 [5,+,4,3,1] => 37 [5,-,4,3,1] => 47 [5,3,1,2,4] => 48 [5,3,1,+,2] => 30 [5,3,1,-,2] => 50 [5,3,2,1,4] => 49 [5,3,2,+,1] => 32 [5,3,2,-,1] => 52 [5,3,4,1,2] => 33 [5,3,4,2,1] => 34 [5,4,1,2,3] => 46 [5,4,1,3,2] => 47 [5,4,2,1,3] => 47 [5,4,2,3,1] => 49 [5,4,+,1,2] => 34 [5,4,-,1,2] => 49 [5,4,+,2,1] => 35 [5,4,-,2,1] => 50 ----------------------------------------------------------------------------- Created: May 14, 2020 at 20:41 by Danny Luecke ----------------------------------------------------------------------------- Last Updated: May 14, 2020 at 20:41 by Danny Luecke