***************************************************************************** * 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: St000531 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The number of ways to place as many non-attacking rooks as possible on a Ferrers board. ----------------------------------------------------------------------------- References: [1] [[wikipedia:Rook_polynomial]] ----------------------------------------------------------------------------- Code: def statistic(la): return (matrix([[1]*p + [0]*(la[0]-p) for p in la]).rook_vector())[-1] ----------------------------------------------------------------------------- Statistic values: [] => 1 [1] => 1 [2] => 2 [1,1] => 2 [3] => 3 [2,1] => 1 [1,1,1] => 3 [4] => 4 [3,1] => 2 [2,2] => 2 [2,1,1] => 2 [1,1,1,1] => 4 [5] => 5 [4,1] => 3 [3,2] => 4 [3,1,1] => 0 [2,2,1] => 4 [2,1,1,1] => 3 [1,1,1,1,1] => 5 [6] => 6 [5,1] => 4 [4,2] => 6 [4,1,1] => 0 [3,3] => 6 [3,2,1] => 1 [3,1,1,1] => 0 [2,2,2] => 6 [2,2,1,1] => 6 [2,1,1,1,1] => 4 [1,1,1,1,1,1] => 6 [7] => 7 [6,1] => 5 [5,2] => 8 [5,1,1] => 0 [4,3] => 9 [4,2,1] => 2 [4,1,1,1] => 0 [3,3,1] => 2 [3,2,2] => 2 [3,2,1,1] => 2 [3,1,1,1,1] => 0 [2,2,2,1] => 9 [2,2,1,1,1] => 8 [2,1,1,1,1,1] => 5 [1,1,1,1,1,1,1] => 7 [8] => 8 [7,1] => 6 [6,2] => 10 [6,1,1] => 0 [5,3] => 12 [5,2,1] => 3 [5,1,1,1] => 0 [4,4] => 12 [4,3,1] => 4 [4,2,2] => 4 [4,2,1,1] => 0 [4,1,1,1,1] => 0 [3,3,2] => 4 [3,3,1,1] => 4 [3,2,2,1] => 4 [3,2,1,1,1] => 3 [3,1,1,1,1,1] => 0 [2,2,2,2] => 12 [2,2,2,1,1] => 12 [2,2,1,1,1,1] => 10 [2,1,1,1,1,1,1] => 6 [1,1,1,1,1,1,1,1] => 8 [9] => 9 [8,1] => 7 [7,2] => 12 [7,1,1] => 0 [6,3] => 15 [6,2,1] => 4 [6,1,1,1] => 0 [5,4] => 16 [5,3,1] => 6 [5,2,2] => 6 [5,2,1,1] => 0 [5,1,1,1,1] => 0 [4,4,1] => 6 [4,3,2] => 8 [4,3,1,1] => 0 [4,2,2,1] => 0 [4,2,1,1,1] => 0 [4,1,1,1,1,1] => 0 [3,3,3] => 6 [3,3,2,1] => 8 [3,3,1,1,1] => 6 [3,2,2,2] => 6 [3,2,2,1,1] => 6 [3,2,1,1,1,1] => 4 [3,1,1,1,1,1,1] => 0 [2,2,2,2,1] => 16 [2,2,2,1,1,1] => 15 [2,2,1,1,1,1,1] => 12 [2,1,1,1,1,1,1,1] => 7 [1,1,1,1,1,1,1,1,1] => 9 [10] => 10 [9,1] => 8 [8,2] => 14 [8,1,1] => 0 [7,3] => 18 [7,2,1] => 5 [7,1,1,1] => 0 [6,4] => 20 [6,3,1] => 8 [6,2,2] => 8 [6,2,1,1] => 0 [6,1,1,1,1] => 0 [5,5] => 20 [5,4,1] => 9 [5,3,2] => 12 [5,3,1,1] => 0 [5,2,2,1] => 0 [5,2,1,1,1] => 0 [5,1,1,1,1,1] => 0 [4,4,2] => 12 [4,4,1,1] => 0 [4,3,3] => 12 [4,3,2,1] => 1 [4,3,1,1,1] => 0 [4,2,2,2] => 0 [4,2,2,1,1] => 0 [4,2,1,1,1,1] => 0 [4,1,1,1,1,1,1] => 0 [3,3,3,1] => 12 [3,3,2,2] => 12 [3,3,2,1,1] => 12 [3,3,1,1,1,1] => 8 [3,2,2,2,1] => 9 [3,2,2,1,1,1] => 8 [3,2,1,1,1,1,1] => 5 [3,1,1,1,1,1,1,1] => 0 [2,2,2,2,2] => 20 [2,2,2,2,1,1] => 20 [2,2,2,1,1,1,1] => 18 [2,2,1,1,1,1,1,1] => 14 [2,1,1,1,1,1,1,1,1] => 8 [1,1,1,1,1,1,1,1,1,1] => 10 [11] => 11 [10,1] => 9 [9,2] => 16 [9,1,1] => 0 [8,3] => 21 [8,2,1] => 6 [8,1,1,1] => 0 [7,4] => 24 [7,3,1] => 10 [7,2,2] => 10 [7,2,1,1] => 0 [7,1,1,1,1] => 0 [6,5] => 25 [6,4,1] => 12 [6,3,2] => 16 [6,3,1,1] => 0 [6,2,2,1] => 0 [6,2,1,1,1] => 0 [6,1,1,1,1,1] => 0 [5,5,1] => 12 [5,4,2] => 18 [5,4,1,1] => 0 [5,3,3] => 18 [5,3,2,1] => 2 [5,3,1,1,1] => 0 [5,2,2,2] => 0 [5,2,2,1,1] => 0 [5,2,1,1,1,1] => 0 [5,1,1,1,1,1,1] => 0 [4,4,3] => 18 [4,4,2,1] => 2 [4,4,1,1,1] => 0 [4,3,3,1] => 2 [4,3,2,2] => 2 [4,3,2,1,1] => 2 [4,3,1,1,1,1] => 0 [4,2,2,2,1] => 0 [4,2,2,1,1,1] => 0 [4,2,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1] => 0 [3,3,3,2] => 18 [3,3,3,1,1] => 18 [3,3,2,2,1] => 18 [3,3,2,1,1,1] => 16 [3,3,1,1,1,1,1] => 10 [3,2,2,2,2] => 12 [3,2,2,2,1,1] => 12 [3,2,2,1,1,1,1] => 10 [3,2,1,1,1,1,1,1] => 6 [3,1,1,1,1,1,1,1,1] => 0 [2,2,2,2,2,1] => 25 [2,2,2,2,1,1,1] => 24 [2,2,2,1,1,1,1,1] => 21 [2,2,1,1,1,1,1,1,1] => 16 [2,1,1,1,1,1,1,1,1,1] => 9 [1,1,1,1,1,1,1,1,1,1,1] => 11 [12] => 12 [11,1] => 10 [10,2] => 18 [10,1,1] => 0 [9,3] => 24 [9,2,1] => 7 [9,1,1,1] => 0 [8,4] => 28 [8,3,1] => 12 [8,2,2] => 12 [8,2,1,1] => 0 [8,1,1,1,1] => 0 [7,5] => 30 [7,4,1] => 15 [7,3,2] => 20 [7,3,1,1] => 0 [7,2,2,1] => 0 [7,2,1,1,1] => 0 [7,1,1,1,1,1] => 0 [6,6] => 30 [6,5,1] => 16 [6,4,2] => 24 [6,4,1,1] => 0 [6,3,3] => 24 [6,3,2,1] => 3 [6,3,1,1,1] => 0 [6,2,2,2] => 0 [6,2,2,1,1] => 0 [6,2,1,1,1,1] => 0 [6,1,1,1,1,1,1] => 0 [5,5,2] => 24 [5,5,1,1] => 0 [5,4,3] => 27 [5,4,2,1] => 4 [5,4,1,1,1] => 0 [5,3,3,1] => 4 [5,3,2,2] => 4 [5,3,2,1,1] => 0 [5,3,1,1,1,1] => 0 [5,2,2,2,1] => 0 [5,2,2,1,1,1] => 0 [5,2,1,1,1,1,1] => 0 [5,1,1,1,1,1,1,1] => 0 [4,4,4] => 24 [4,4,3,1] => 4 [4,4,2,2] => 4 [4,4,2,1,1] => 4 [4,4,1,1,1,1] => 0 [4,3,3,2] => 4 [4,3,3,1,1] => 4 [4,3,2,2,1] => 4 [4,3,2,1,1,1] => 3 [4,3,1,1,1,1,1] => 0 [4,2,2,2,2] => 0 [4,2,2,2,1,1] => 0 [4,2,2,1,1,1,1] => 0 [4,2,1,1,1,1,1,1] => 0 [4,1,1,1,1,1,1,1,1] => 0 [3,3,3,3] => 24 [3,3,3,2,1] => 27 [3,3,3,1,1,1] => 24 [3,3,2,2,2] => 24 [3,3,2,2,1,1] => 24 [3,3,2,1,1,1,1] => 20 [3,3,1,1,1,1,1,1] => 12 [3,2,2,2,2,1] => 16 [3,2,2,2,1,1,1] => 15 [3,2,2,1,1,1,1,1] => 12 [3,2,1,1,1,1,1,1,1] => 7 [3,1,1,1,1,1,1,1,1,1] => 0 [2,2,2,2,2,2] => 30 [2,2,2,2,2,1,1] => 30 [2,2,2,2,1,1,1,1] => 28 [2,2,2,1,1,1,1,1,1] => 24 [2,2,1,1,1,1,1,1,1,1] => 18 [2,1,1,1,1,1,1,1,1,1,1] => 10 [1,1,1,1,1,1,1,1,1,1,1,1] => 12 ----------------------------------------------------------------------------- Created: Jun 10, 2016 at 23:50 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Oct 29, 2017 at 21:31 by Martin Rubey