***************************************************************************** * 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: St000108 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The number of partitions contained in the given partition. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(L): return sum( 1 for n in range(L.size()) for P in Partitions(n) if L.contains(P) ) + 1 ----------------------------------------------------------------------------- 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] => 6 [2,1,1] => 7 [1,1,1,1] => 5 [5] => 6 [4,1] => 9 [3,2] => 9 [3,1,1] => 10 [2,2,1] => 9 [2,1,1,1] => 9 [1,1,1,1,1] => 6 [6] => 7 [5,1] => 11 [4,2] => 12 [4,1,1] => 13 [3,3] => 10 [3,2,1] => 14 [3,1,1,1] => 13 [2,2,2] => 10 [2,2,1,1] => 12 [2,1,1,1,1] => 11 [1,1,1,1,1,1] => 7 [7] => 8 [6,1] => 13 [5,2] => 15 [5,1,1] => 16 [4,3] => 14 [4,2,1] => 19 [4,1,1,1] => 17 [3,3,1] => 16 [3,2,2] => 16 [3,2,1,1] => 19 [3,1,1,1,1] => 16 [2,2,2,1] => 14 [2,2,1,1,1] => 15 [2,1,1,1,1,1] => 13 [1,1,1,1,1,1,1] => 8 [8] => 9 [7,1] => 15 [6,2] => 18 [6,1,1] => 19 [5,3] => 18 [5,2,1] => 24 [5,1,1,1] => 21 [4,4] => 15 [4,3,1] => 23 [4,2,2] => 22 [4,2,1,1] => 26 [4,1,1,1,1] => 21 [3,3,2] => 19 [3,3,1,1] => 22 [3,2,2,1] => 23 [3,2,1,1,1] => 24 [3,1,1,1,1,1] => 19 [2,2,2,2] => 15 [2,2,2,1,1] => 18 [2,2,1,1,1,1] => 18 [2,1,1,1,1,1,1] => 15 [1,1,1,1,1,1,1,1] => 9 [9] => 10 [8,1] => 17 [7,2] => 21 [7,1,1] => 22 [6,3] => 22 [6,2,1] => 29 [6,1,1,1] => 25 [5,4] => 20 [5,3,1] => 30 [5,2,2] => 28 [5,2,1,1] => 33 [5,1,1,1,1] => 26 [4,4,1] => 25 [4,3,2] => 28 [4,3,1,1] => 32 [4,2,2,1] => 32 [4,2,1,1,1] => 33 [4,1,1,1,1,1] => 25 [3,3,3] => 20 [3,3,2,1] => 28 [3,3,1,1,1] => 28 [3,2,2,2] => 25 [3,2,2,1,1] => 30 [3,2,1,1,1,1] => 29 [3,1,1,1,1,1,1] => 22 [2,2,2,2,1] => 20 [2,2,2,1,1,1] => 22 [2,2,1,1,1,1,1] => 21 [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] => 24 [8,1,1] => 25 [7,3] => 26 [7,2,1] => 34 [7,1,1,1] => 29 [6,4] => 25 [6,3,1] => 37 [6,2,2] => 34 [6,2,1,1] => 40 [6,1,1,1,1] => 31 [5,5] => 21 [5,4,1] => 34 [5,3,2] => 37 [5,3,1,1] => 42 [5,2,2,1] => 41 [5,2,1,1,1] => 42 [5,1,1,1,1,1] => 31 [4,4,2] => 31 [4,4,1,1] => 35 [4,3,3] => 30 [4,3,2,1] => 42 [4,3,1,1,1] => 41 [4,2,2,2] => 35 [4,2,2,1,1] => 42 [4,2,1,1,1,1] => 40 [4,1,1,1,1,1,1] => 29 [3,3,3,1] => 30 [3,3,2,2] => 31 [3,3,2,1,1] => 37 [3,3,1,1,1,1] => 34 [3,2,2,2,1] => 34 [3,2,2,1,1,1] => 37 [3,2,1,1,1,1,1] => 34 [3,1,1,1,1,1,1,1] => 25 [2,2,2,2,2] => 21 [2,2,2,2,1,1] => 25 [2,2,2,1,1,1,1] => 26 [2,2,1,1,1,1,1,1] => 24 [2,1,1,1,1,1,1,1,1] => 19 [1,1,1,1,1,1,1,1,1,1] => 11 ----------------------------------------------------------------------------- Created: Jun 15, 2013 at 13:18 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Oct 29, 2017 at 16:05 by Martin Rubey