***************************************************************************** * 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: St000049 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The number of set partitions whose sorted block sizes correspond to the partition. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(L): return len( [ S for S in SetPartitions(L.size()) if S.to_partition() == L ] ) ----------------------------------------------------------------------------- Statistic values: [] => 1 [1] => 1 [2] => 1 [1,1] => 1 [3] => 1 [2,1] => 3 [1,1,1] => 1 [4] => 1 [3,1] => 4 [2,2] => 3 [2,1,1] => 6 [1,1,1,1] => 1 [5] => 1 [4,1] => 5 [3,2] => 10 [3,1,1] => 10 [2,2,1] => 15 [2,1,1,1] => 10 [1,1,1,1,1] => 1 [6] => 1 [5,1] => 6 [4,2] => 15 [4,1,1] => 15 [3,3] => 10 [3,2,1] => 60 [3,1,1,1] => 20 [2,2,2] => 15 [2,2,1,1] => 45 [2,1,1,1,1] => 15 [1,1,1,1,1,1] => 1 [7] => 1 [6,1] => 7 [5,2] => 21 [5,1,1] => 21 [4,3] => 35 [4,2,1] => 105 [4,1,1,1] => 35 [3,3,1] => 70 [3,2,2] => 105 [3,2,1,1] => 210 [3,1,1,1,1] => 35 [2,2,2,1] => 105 [2,2,1,1,1] => 105 [2,1,1,1,1,1] => 21 [1,1,1,1,1,1,1] => 1 [8] => 1 [7,1] => 8 [6,2] => 28 [6,1,1] => 28 [5,3] => 56 [5,2,1] => 168 [5,1,1,1] => 56 [4,4] => 35 [4,3,1] => 280 [4,2,2] => 210 [4,2,1,1] => 420 [4,1,1,1,1] => 70 [3,3,2] => 280 [3,3,1,1] => 280 [3,2,2,1] => 840 [3,2,1,1,1] => 560 [3,1,1,1,1,1] => 56 [2,2,2,2] => 105 [2,2,2,1,1] => 420 [2,2,1,1,1,1] => 210 [2,1,1,1,1,1,1] => 28 [1,1,1,1,1,1,1,1] => 1 [9] => 1 [8,1] => 9 [7,2] => 36 [7,1,1] => 36 [6,3] => 84 [6,2,1] => 252 [6,1,1,1] => 84 [5,4] => 126 [5,3,1] => 504 [5,2,2] => 378 [5,2,1,1] => 756 [5,1,1,1,1] => 126 [4,4,1] => 315 [4,3,2] => 1260 [4,3,1,1] => 1260 [4,2,2,1] => 1890 [4,2,1,1,1] => 1260 [4,1,1,1,1,1] => 126 [3,3,3] => 280 [3,3,2,1] => 2520 [3,3,1,1,1] => 840 [3,2,2,2] => 1260 [3,2,2,1,1] => 3780 [3,2,1,1,1,1] => 1260 [3,1,1,1,1,1,1] => 84 [2,2,2,2,1] => 945 [2,2,2,1,1,1] => 1260 [2,2,1,1,1,1,1] => 378 [2,1,1,1,1,1,1,1] => 36 [1,1,1,1,1,1,1,1,1] => 1 [10] => 1 [9,1] => 10 [8,2] => 45 [8,1,1] => 45 [7,3] => 120 [7,2,1] => 360 [7,1,1,1] => 120 [6,4] => 210 [6,3,1] => 840 [6,2,2] => 630 [6,2,1,1] => 1260 [6,1,1,1,1] => 210 [5,5] => 126 [5,4,1] => 1260 [5,3,2] => 2520 [5,3,1,1] => 2520 [5,2,2,1] => 3780 [5,2,1,1,1] => 2520 [5,1,1,1,1,1] => 252 [4,4,2] => 1575 [4,4,1,1] => 1575 [4,3,3] => 2100 [4,3,2,1] => 12600 [4,3,1,1,1] => 4200 [4,2,2,2] => 3150 [4,2,2,1,1] => 9450 [4,2,1,1,1,1] => 3150 [4,1,1,1,1,1,1] => 210 [3,3,3,1] => 2800 [3,3,2,2] => 6300 [3,3,2,1,1] => 12600 [3,3,1,1,1,1] => 2100 [3,2,2,2,1] => 12600 [3,2,2,1,1,1] => 12600 [3,2,1,1,1,1,1] => 2520 [3,1,1,1,1,1,1,1] => 120 [2,2,2,2,2] => 945 [2,2,2,2,1,1] => 4725 [2,2,2,1,1,1,1] => 3150 [2,2,1,1,1,1,1,1] => 630 [2,1,1,1,1,1,1,1,1] => 45 [1,1,1,1,1,1,1,1,1,1] => 1 ----------------------------------------------------------------------------- Created: Mar 25, 2013 at 10:03 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Oct 29, 2017 at 20:28 by Martin Rubey