***************************************************************************** * 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: St000532 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The total number of rook placements on a Ferrers board. ----------------------------------------------------------------------------- References: [1] [[wikipedia:Rook_polynomial]] ----------------------------------------------------------------------------- Code: def statistic(la): return sum(matrix([[1]*p + [0]*(la[0]-p) for p in la]).rook_vector()) ----------------------------------------------------------------------------- Statistic values: [] => 1 [1] => 2 [2] => 3 [1,1] => 3 [3] => 4 [2,1] => 5 [1,1,1] => 4 [4] => 5 [3,1] => 7 [2,2] => 7 [2,1,1] => 7 [1,1,1,1] => 5 [5] => 6 [4,1] => 9 [3,2] => 10 [3,1,1] => 10 [2,2,1] => 10 [2,1,1,1] => 9 [1,1,1,1,1] => 6 [6] => 7 [5,1] => 11 [4,2] => 13 [4,1,1] => 13 [3,3] => 13 [3,2,1] => 15 [3,1,1,1] => 13 [2,2,2] => 13 [2,2,1,1] => 13 [2,1,1,1,1] => 11 [1,1,1,1,1,1] => 7 [7] => 8 [6,1] => 13 [5,2] => 16 [5,1,1] => 16 [4,3] => 17 [4,2,1] => 20 [4,1,1,1] => 17 [3,3,1] => 20 [3,2,2] => 20 [3,2,1,1] => 20 [3,1,1,1,1] => 16 [2,2,2,1] => 17 [2,2,1,1,1] => 16 [2,1,1,1,1,1] => 13 [1,1,1,1,1,1,1] => 8 [8] => 9 [7,1] => 15 [6,2] => 19 [6,1,1] => 19 [5,3] => 21 [5,2,1] => 25 [5,1,1,1] => 21 [4,4] => 21 [4,3,1] => 27 [4,2,2] => 27 [4,2,1,1] => 27 [4,1,1,1,1] => 21 [3,3,2] => 27 [3,3,1,1] => 27 [3,2,2,1] => 27 [3,2,1,1,1] => 25 [3,1,1,1,1,1] => 19 [2,2,2,2] => 21 [2,2,2,1,1] => 21 [2,2,1,1,1,1] => 19 [2,1,1,1,1,1,1] => 15 [1,1,1,1,1,1,1,1] => 9 [9] => 10 [8,1] => 17 [7,2] => 22 [7,1,1] => 22 [6,3] => 25 [6,2,1] => 30 [6,1,1,1] => 25 [5,4] => 26 [5,3,1] => 34 [5,2,2] => 34 [5,2,1,1] => 34 [5,1,1,1,1] => 26 [4,4,1] => 34 [4,3,2] => 37 [4,3,1,1] => 37 [4,2,2,1] => 37 [4,2,1,1,1] => 34 [4,1,1,1,1,1] => 25 [3,3,3] => 34 [3,3,2,1] => 37 [3,3,1,1,1] => 34 [3,2,2,2] => 34 [3,2,2,1,1] => 34 [3,2,1,1,1,1] => 30 [3,1,1,1,1,1,1] => 22 [2,2,2,2,1] => 26 [2,2,2,1,1,1] => 25 [2,2,1,1,1,1,1] => 22 [2,1,1,1,1,1,1,1] => 17 [1,1,1,1,1,1,1,1,1] => 10 [10] => 11 [9,1] => 19 [8,2] => 25 [8,1,1] => 25 [7,3] => 29 [7,2,1] => 35 [7,1,1,1] => 29 [6,4] => 31 [6,3,1] => 41 [6,2,2] => 41 [6,2,1,1] => 41 [6,1,1,1,1] => 31 [5,5] => 31 [5,4,1] => 43 [5,3,2] => 47 [5,3,1,1] => 47 [5,2,2,1] => 47 [5,2,1,1,1] => 43 [5,1,1,1,1,1] => 31 [4,4,2] => 47 [4,4,1,1] => 47 [4,3,3] => 47 [4,3,2,1] => 52 [4,3,1,1,1] => 47 [4,2,2,2] => 47 [4,2,2,1,1] => 47 [4,2,1,1,1,1] => 41 [4,1,1,1,1,1,1] => 29 [3,3,3,1] => 47 [3,3,2,2] => 47 [3,3,2,1,1] => 47 [3,3,1,1,1,1] => 41 [3,2,2,2,1] => 43 [3,2,2,1,1,1] => 41 [3,2,1,1,1,1,1] => 35 [3,1,1,1,1,1,1,1] => 25 [2,2,2,2,2] => 31 [2,2,2,2,1,1] => 31 [2,2,2,1,1,1,1] => 29 [2,2,1,1,1,1,1,1] => 25 [2,1,1,1,1,1,1,1,1] => 19 [1,1,1,1,1,1,1,1,1,1] => 11 [11] => 12 [10,1] => 21 [9,2] => 28 [9,1,1] => 28 [8,3] => 33 [8,2,1] => 40 [8,1,1,1] => 33 [7,4] => 36 [7,3,1] => 48 [7,2,2] => 48 [7,2,1,1] => 48 [7,1,1,1,1] => 36 [6,5] => 37 [6,4,1] => 52 [6,3,2] => 57 [6,3,1,1] => 57 [6,2,2,1] => 57 [6,2,1,1,1] => 52 [6,1,1,1,1,1] => 37 [5,5,1] => 52 [5,4,2] => 60 [5,4,1,1] => 60 [5,3,3] => 60 [5,3,2,1] => 67 [5,3,1,1,1] => 60 [5,2,2,2] => 60 [5,2,2,1,1] => 60 [5,2,1,1,1,1] => 52 [5,1,1,1,1,1,1] => 36 [4,4,3] => 60 [4,4,2,1] => 67 [4,4,1,1,1] => 60 [4,3,3,1] => 67 [4,3,2,2] => 67 [4,3,2,1,1] => 67 [4,3,1,1,1,1] => 57 [4,2,2,2,1] => 60 [4,2,2,1,1,1] => 57 [4,2,1,1,1,1,1] => 48 [4,1,1,1,1,1,1,1] => 33 [3,3,3,2] => 60 [3,3,3,1,1] => 60 [3,3,2,2,1] => 60 [3,3,2,1,1,1] => 57 [3,3,1,1,1,1,1] => 48 [3,2,2,2,2] => 52 [3,2,2,2,1,1] => 52 [3,2,2,1,1,1,1] => 48 [3,2,1,1,1,1,1,1] => 40 [3,1,1,1,1,1,1,1,1] => 28 [2,2,2,2,2,1] => 37 [2,2,2,2,1,1,1] => 36 [2,2,2,1,1,1,1,1] => 33 [2,2,1,1,1,1,1,1,1] => 28 [2,1,1,1,1,1,1,1,1,1] => 21 [1,1,1,1,1,1,1,1,1,1,1] => 12 [12] => 13 [11,1] => 23 [10,2] => 31 [10,1,1] => 31 [9,3] => 37 [9,2,1] => 45 [9,1,1,1] => 37 [8,4] => 41 [8,3,1] => 55 [8,2,2] => 55 [8,2,1,1] => 55 [8,1,1,1,1] => 41 [7,5] => 43 [7,4,1] => 61 [7,3,2] => 67 [7,3,1,1] => 67 [7,2,2,1] => 67 [7,2,1,1,1] => 61 [7,1,1,1,1,1] => 43 [6,6] => 43 [6,5,1] => 63 [6,4,2] => 73 [6,4,1,1] => 73 [6,3,3] => 73 [6,3,2,1] => 82 [6,3,1,1,1] => 73 [6,2,2,2] => 73 [6,2,2,1,1] => 73 [6,2,1,1,1,1] => 63 [6,1,1,1,1,1,1] => 43 [5,5,2] => 73 [5,5,1,1] => 73 [5,4,3] => 77 [5,4,2,1] => 87 [5,4,1,1,1] => 77 [5,3,3,1] => 87 [5,3,2,2] => 87 [5,3,2,1,1] => 87 [5,3,1,1,1,1] => 73 [5,2,2,2,1] => 77 [5,2,2,1,1,1] => 73 [5,2,1,1,1,1,1] => 61 [5,1,1,1,1,1,1,1] => 41 [4,4,4] => 73 [4,4,3,1] => 87 [4,4,2,2] => 87 [4,4,2,1,1] => 87 [4,4,1,1,1,1] => 73 [4,3,3,2] => 87 [4,3,3,1,1] => 87 [4,3,2,2,1] => 87 [4,3,2,1,1,1] => 82 [4,3,1,1,1,1,1] => 67 [4,2,2,2,2] => 73 [4,2,2,2,1,1] => 73 [4,2,2,1,1,1,1] => 67 [4,2,1,1,1,1,1,1] => 55 [4,1,1,1,1,1,1,1,1] => 37 [3,3,3,3] => 73 [3,3,3,2,1] => 77 [3,3,3,1,1,1] => 73 [3,3,2,2,2] => 73 [3,3,2,2,1,1] => 73 [3,3,2,1,1,1,1] => 67 [3,3,1,1,1,1,1,1] => 55 [3,2,2,2,2,1] => 63 [3,2,2,2,1,1,1] => 61 [3,2,2,1,1,1,1,1] => 55 [3,2,1,1,1,1,1,1,1] => 45 [3,1,1,1,1,1,1,1,1,1] => 31 [2,2,2,2,2,2] => 43 [2,2,2,2,2,1,1] => 43 [2,2,2,2,1,1,1,1] => 41 [2,2,2,1,1,1,1,1,1] => 37 [2,2,1,1,1,1,1,1,1,1] => 31 [2,1,1,1,1,1,1,1,1,1,1] => 23 [1,1,1,1,1,1,1,1,1,1,1,1] => 13 [5,4,3,1] => 114 [5,4,2,2] => 114 [5,4,2,1,1] => 114 [5,3,3,2] => 114 [5,3,3,1,1] => 114 [5,3,2,2,1] => 114 [4,4,3,2] => 114 [4,4,3,1,1] => 114 [4,4,2,2,1] => 114 [4,3,3,2,1] => 114 [5,4,3,2] => 151 [5,4,3,1,1] => 151 [5,4,2,2,1] => 151 [5,3,3,2,1] => 151 [4,4,3,2,1] => 151 [5,4,3,2,1] => 203 ----------------------------------------------------------------------------- Created: Jun 10, 2016 at 23:59 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Apr 26, 2018 at 07:39 by Martin Rubey