***************************************************************************** * 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: St001538 ----------------------------------------------------------------------------- Collection: Decorated permutations ----------------------------------------------------------------------------- Description: Sum of decorated fixed points as signed integers. Every fixed point decorated with a '+' is treated as a positive integer, and every fixed point decorated with a '-' is treated as a negative integer. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [+,+] => 3 [-,+] => 1 [+,-] => -1 [-,-] => -3 [2,1] => 0 [+,+,+] => 6 [-,+,+] => 4 [+,-,+] => 2 [+,+,-] => 0 [-,-,+] => 0 [-,+,-] => -2 [+,-,-] => -4 [-,-,-] => -6 [+,3,2] => 1 [-,3,2] => -1 [2,1,+] => 3 [2,1,-] => -3 [2,3,1] => 0 [3,1,2] => 0 [3,+,1] => 2 [3,-,1] => -2 [+,+,+,+] => 10 [-,+,+,+] => 8 [+,-,+,+] => 6 [+,+,-,+] => 4 [+,+,+,-] => 2 [-,-,+,+] => 4 [-,+,-,+] => 2 [-,+,+,-] => 0 [+,-,-,+] => 0 [+,-,+,-] => -2 [+,+,-,-] => -4 [-,-,-,+] => -2 [-,-,+,-] => -4 [-,+,-,-] => -6 [+,-,-,-] => -8 [-,-,-,-] => -10 [+,+,4,3] => 3 [-,+,4,3] => 1 [+,-,4,3] => -1 [-,-,4,3] => -3 [+,3,2,+] => 5 [-,3,2,+] => 3 [+,3,2,-] => -3 [-,3,2,-] => -5 [+,3,4,2] => 1 [-,3,4,2] => -1 [+,4,2,3] => 1 [-,4,2,3] => -1 [+,4,+,2] => 4 [-,4,+,2] => 2 [+,4,-,2] => -2 [-,4,-,2] => -4 [2,1,+,+] => 7 [2,1,-,+] => 1 [2,1,+,-] => -1 [2,1,-,-] => -7 [2,1,4,3] => 0 [2,3,1,+] => 4 [2,3,1,-] => -4 [2,3,4,1] => 0 [2,4,1,3] => 0 [2,4,+,1] => 3 [2,4,-,1] => -3 [3,1,2,+] => 4 [3,1,2,-] => -4 [3,1,4,2] => 0 [3,+,1,+] => 6 [3,-,1,+] => 2 [3,+,1,-] => -2 [3,-,1,-] => -6 [3,+,4,1] => 2 [3,-,4,1] => -2 [3,4,1,2] => 0 [3,4,2,1] => 0 [4,1,2,3] => 0 [4,1,+,2] => 3 [4,1,-,2] => -3 [4,+,1,3] => 2 [4,-,1,3] => -2 [4,+,+,1] => 5 [4,-,+,1] => 1 [4,+,-,1] => -1 [4,-,-,1] => -5 [4,3,1,2] => 0 [4,3,2,1] => 0 [+,+,+,+,+] => 15 [-,+,+,+,+] => 13 [+,-,+,+,+] => 11 [+,+,-,+,+] => 9 [+,+,+,-,+] => 7 [+,+,+,+,-] => 5 [-,-,+,+,+] => 9 [-,+,-,+,+] => 7 [-,+,+,-,+] => 5 [-,+,+,+,-] => 3 [+,-,-,+,+] => 5 [+,-,+,-,+] => 3 [+,-,+,+,-] => 1 [+,+,-,-,+] => 1 [+,+,-,+,-] => -1 [+,+,+,-,-] => -3 [-,-,-,+,+] => 3 [-,-,+,-,+] => 1 [-,-,+,+,-] => -1 [-,+,-,-,+] => -1 [-,+,-,+,-] => -3 [-,+,+,-,-] => -5 [+,-,-,-,+] => -3 [+,-,-,+,-] => -5 [+,-,+,-,-] => -7 [+,+,-,-,-] => -9 [-,-,-,-,+] => -5 [-,-,-,+,-] => -7 [-,-,+,-,-] => -9 [-,+,-,-,-] => -11 [+,-,-,-,-] => -13 [-,-,-,-,-] => -15 [+,+,+,5,4] => 6 [-,+,+,5,4] => 4 [+,-,+,5,4] => 2 [+,+,-,5,4] => 0 [-,-,+,5,4] => 0 [-,+,-,5,4] => -2 [+,-,-,5,4] => -4 [-,-,-,5,4] => -6 [+,+,4,3,+] => 8 [-,+,4,3,+] => 6 [+,-,4,3,+] => 4 [+,+,4,3,-] => -2 [-,-,4,3,+] => 2 [-,+,4,3,-] => -4 [+,-,4,3,-] => -6 [-,-,4,3,-] => -8 [+,+,4,5,3] => 3 [-,+,4,5,3] => 1 [+,-,4,5,3] => -1 [-,-,4,5,3] => -3 [+,+,5,3,4] => 3 [-,+,5,3,4] => 1 [+,-,5,3,4] => -1 [-,-,5,3,4] => -3 [+,+,5,+,3] => 7 [-,+,5,+,3] => 5 [+,-,5,+,3] => 3 [+,+,5,-,3] => -1 [-,-,5,+,3] => 1 [-,+,5,-,3] => -3 [+,-,5,-,3] => -5 [-,-,5,-,3] => -7 [+,3,2,+,+] => 10 [-,3,2,+,+] => 8 [+,3,2,-,+] => 2 [+,3,2,+,-] => 0 [-,3,2,-,+] => 0 [-,3,2,+,-] => -2 [+,3,2,-,-] => -8 [-,3,2,-,-] => -10 [+,3,2,5,4] => 1 [-,3,2,5,4] => -1 [+,3,4,2,+] => 6 [-,3,4,2,+] => 4 [+,3,4,2,-] => -4 [-,3,4,2,-] => -6 [+,3,4,5,2] => 1 [-,3,4,5,2] => -1 [+,3,5,2,4] => 1 [-,3,5,2,4] => -1 [+,3,5,+,2] => 5 [-,3,5,+,2] => 3 [+,3,5,-,2] => -3 [-,3,5,-,2] => -5 [+,4,2,3,+] => 6 [-,4,2,3,+] => 4 [+,4,2,3,-] => -4 [-,4,2,3,-] => -6 [+,4,2,5,3] => 1 [-,4,2,5,3] => -1 [+,4,+,2,+] => 9 [-,4,+,2,+] => 7 [+,4,-,2,+] => 3 [+,4,+,2,-] => -1 [-,4,-,2,+] => 1 [-,4,+,2,-] => -3 [+,4,-,2,-] => -7 [-,4,-,2,-] => -9 [+,4,+,5,2] => 4 [-,4,+,5,2] => 2 [+,4,-,5,2] => -2 [-,4,-,5,2] => -4 [+,4,5,2,3] => 1 [-,4,5,2,3] => -1 [+,4,5,3,2] => 1 [-,4,5,3,2] => -1 [+,5,2,3,4] => 1 [-,5,2,3,4] => -1 [+,5,2,+,3] => 5 [-,5,2,+,3] => 3 [+,5,2,-,3] => -3 [-,5,2,-,3] => -5 [+,5,+,2,4] => 4 [-,5,+,2,4] => 2 [+,5,-,2,4] => -2 [-,5,-,2,4] => -4 [+,5,+,+,2] => 8 [-,5,+,+,2] => 6 [+,5,-,+,2] => 2 [+,5,+,-,2] => 0 [-,5,-,+,2] => 0 [-,5,+,-,2] => -2 [+,5,-,-,2] => -6 [-,5,-,-,2] => -8 [+,5,4,2,3] => 1 [-,5,4,2,3] => -1 [+,5,4,3,2] => 1 [-,5,4,3,2] => -1 [2,1,+,+,+] => 12 [2,1,-,+,+] => 6 [2,1,+,-,+] => 4 [2,1,+,+,-] => 2 [2,1,-,-,+] => -2 [2,1,-,+,-] => -4 [2,1,+,-,-] => -6 [2,1,-,-,-] => -12 [2,1,+,5,4] => 3 [2,1,-,5,4] => -3 [2,1,4,3,+] => 5 [2,1,4,3,-] => -5 [2,1,4,5,3] => 0 [2,1,5,3,4] => 0 [2,1,5,+,3] => 4 [2,1,5,-,3] => -4 [2,3,1,+,+] => 9 [2,3,1,-,+] => 1 [2,3,1,+,-] => -1 [2,3,1,-,-] => -9 [2,3,1,5,4] => 0 [2,3,4,1,+] => 5 [2,3,4,1,-] => -5 [2,3,4,5,1] => 0 [2,3,5,1,4] => 0 [2,3,5,+,1] => 4 [2,3,5,-,1] => -4 [2,4,1,3,+] => 5 [2,4,1,3,-] => -5 [2,4,1,5,3] => 0 [2,4,+,1,+] => 8 [2,4,-,1,+] => 2 [2,4,+,1,-] => -2 [2,4,-,1,-] => -8 [2,4,+,5,1] => 3 [2,4,-,5,1] => -3 [2,4,5,1,3] => 0 [2,4,5,3,1] => 0 [2,5,1,3,4] => 0 [2,5,1,+,3] => 4 [2,5,1,-,3] => -4 [2,5,+,1,4] => 3 [2,5,-,1,4] => -3 [2,5,+,+,1] => 7 [2,5,-,+,1] => 1 [2,5,+,-,1] => -1 [2,5,-,-,1] => -7 [2,5,4,1,3] => 0 [2,5,4,3,1] => 0 [3,1,2,+,+] => 9 [3,1,2,-,+] => 1 [3,1,2,+,-] => -1 [3,1,2,-,-] => -9 [3,1,2,5,4] => 0 [3,1,4,2,+] => 5 [3,1,4,2,-] => -5 [3,1,4,5,2] => 0 [3,1,5,2,4] => 0 [3,1,5,+,2] => 4 [3,1,5,-,2] => -4 [3,+,1,+,+] => 11 [3,-,1,+,+] => 7 [3,+,1,-,+] => 3 [3,+,1,+,-] => 1 [3,-,1,-,+] => -1 [3,-,1,+,-] => -3 [3,+,1,-,-] => -7 [3,-,1,-,-] => -11 [3,+,1,5,4] => 2 [3,-,1,5,4] => -2 [3,+,4,1,+] => 7 [3,-,4,1,+] => 3 [3,+,4,1,-] => -3 [3,-,4,1,-] => -7 [3,+,4,5,1] => 2 [3,-,4,5,1] => -2 [3,+,5,1,4] => 2 [3,-,5,1,4] => -2 [3,+,5,+,1] => 6 [3,-,5,+,1] => 2 [3,+,5,-,1] => -2 [3,-,5,-,1] => -6 [3,4,1,2,+] => 5 [3,4,1,2,-] => -5 [3,4,1,5,2] => 0 [3,4,2,1,+] => 5 [3,4,2,1,-] => -5 [3,4,2,5,1] => 0 [3,4,5,1,2] => 0 [3,4,5,2,1] => 0 [3,5,1,2,4] => 0 [3,5,1,+,2] => 4 [3,5,1,-,2] => -4 [3,5,2,1,4] => 0 [3,5,2,+,1] => 4 [3,5,2,-,1] => -4 [3,5,4,1,2] => 0 [3,5,4,2,1] => 0 [4,1,2,3,+] => 5 [4,1,2,3,-] => -5 [4,1,2,5,3] => 0 [4,1,+,2,+] => 8 [4,1,-,2,+] => 2 [4,1,+,2,-] => -2 [4,1,-,2,-] => -8 [4,1,+,5,2] => 3 [4,1,-,5,2] => -3 [4,1,5,2,3] => 0 [4,1,5,3,2] => 0 [4,+,1,3,+] => 7 [4,-,1,3,+] => 3 [4,+,1,3,-] => -3 [4,-,1,3,-] => -7 [4,+,1,5,3] => 2 [4,-,1,5,3] => -2 [4,+,+,1,+] => 10 [4,-,+,1,+] => 6 [4,+,-,1,+] => 4 [4,+,+,1,-] => 0 [4,-,-,1,+] => 0 [4,-,+,1,-] => -4 [4,+,-,1,-] => -6 [4,-,-,1,-] => -10 [4,+,+,5,1] => 5 [4,-,+,5,1] => 1 [4,+,-,5,1] => -1 [4,-,-,5,1] => -5 [4,+,5,1,3] => 2 [4,-,5,1,3] => -2 [4,+,5,3,1] => 2 [4,-,5,3,1] => -2 [4,3,1,2,+] => 5 [4,3,1,2,-] => -5 [4,3,1,5,2] => 0 [4,3,2,1,+] => 5 [4,3,2,1,-] => -5 [4,3,2,5,1] => 0 [4,3,5,1,2] => 0 [4,3,5,2,1] => 0 [4,5,1,2,3] => 0 [4,5,1,3,2] => 0 [4,5,2,1,3] => 0 [4,5,2,3,1] => 0 [4,5,+,1,2] => 3 [4,5,-,1,2] => -3 [4,5,+,2,1] => 3 [4,5,-,2,1] => -3 [5,1,2,3,4] => 0 [5,1,2,+,3] => 4 [5,1,2,-,3] => -4 [5,1,+,2,4] => 3 [5,1,-,2,4] => -3 [5,1,+,+,2] => 7 [5,1,-,+,2] => 1 [5,1,+,-,2] => -1 [5,1,-,-,2] => -7 [5,1,4,2,3] => 0 [5,1,4,3,2] => 0 [5,+,1,3,4] => 2 [5,-,1,3,4] => -2 [5,+,1,+,3] => 6 [5,-,1,+,3] => 2 [5,+,1,-,3] => -2 [5,-,1,-,3] => -6 [5,+,+,1,4] => 5 [5,-,+,1,4] => 1 [5,+,-,1,4] => -1 [5,-,-,1,4] => -5 [5,+,+,+,1] => 9 [5,-,+,+,1] => 5 [5,+,-,+,1] => 3 [5,+,+,-,1] => 1 [5,-,-,+,1] => -1 [5,-,+,-,1] => -3 [5,+,-,-,1] => -5 [5,-,-,-,1] => -9 [5,+,4,1,3] => 2 [5,-,4,1,3] => -2 [5,+,4,3,1] => 2 [5,-,4,3,1] => -2 [5,3,1,2,4] => 0 [5,3,1,+,2] => 4 [5,3,1,-,2] => -4 [5,3,2,1,4] => 0 [5,3,2,+,1] => 4 [5,3,2,-,1] => -4 [5,3,4,1,2] => 0 [5,3,4,2,1] => 0 [5,4,1,2,3] => 0 [5,4,1,3,2] => 0 [5,4,2,1,3] => 0 [5,4,2,3,1] => 0 [5,4,+,1,2] => 3 [5,4,-,1,2] => -3 [5,4,+,2,1] => 3 [5,4,-,2,1] => -3 ----------------------------------------------------------------------------- Created: May 11, 2020 at 18:39 by James Thorne ----------------------------------------------------------------------------- Last Updated: May 11, 2020 at 18:39 by James Thorne