***************************************************************************** * 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: St000549 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The number of odd partial sums of an integer partition. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(l): return len(set(sum(l[i] for i in X) for X in Subsets(range(len(l))) if is_odd(sum(l[i] for i in X)))) ----------------------------------------------------------------------------- Statistic values: [2] => 0 [1,1] => 1 [3] => 1 [2,1] => 2 [1,1,1] => 2 [4] => 0 [3,1] => 2 [2,2] => 0 [2,1,1] => 2 [1,1,1,1] => 2 [5] => 1 [4,1] => 2 [3,2] => 2 [3,1,1] => 3 [2,2,1] => 3 [2,1,1,1] => 3 [1,1,1,1,1] => 3 [6] => 0 [5,1] => 2 [4,2] => 0 [4,1,1] => 2 [3,3] => 1 [3,2,1] => 3 [3,1,1,1] => 3 [2,2,2] => 0 [2,2,1,1] => 3 [2,1,1,1,1] => 3 [1,1,1,1,1,1] => 3 [7] => 1 [6,1] => 2 [5,2] => 2 [5,1,1] => 3 [4,3] => 2 [4,2,1] => 4 [4,1,1,1] => 4 [3,3,1] => 3 [3,2,2] => 3 [3,2,1,1] => 4 [3,1,1,1,1] => 4 [2,2,2,1] => 4 [2,2,1,1,1] => 4 [2,1,1,1,1,1] => 4 [1,1,1,1,1,1,1] => 4 [8] => 0 [7,1] => 2 [6,2] => 0 [6,1,1] => 2 [5,3] => 2 [5,2,1] => 4 [5,1,1,1] => 4 [4,4] => 0 [4,3,1] => 4 [4,2,2] => 0 [4,2,1,1] => 4 [4,1,1,1,1] => 4 [3,3,2] => 2 [3,3,1,1] => 4 [3,2,2,1] => 4 [3,2,1,1,1] => 4 [3,1,1,1,1,1] => 4 [2,2,2,2] => 0 [2,2,2,1,1] => 4 [2,2,1,1,1,1] => 4 [2,1,1,1,1,1,1] => 4 [1,1,1,1,1,1,1,1] => 4 [9] => 1 [8,1] => 2 [7,2] => 2 [7,1,1] => 3 [6,3] => 2 [6,2,1] => 4 [6,1,1,1] => 4 [5,4] => 2 [5,3,1] => 4 [5,2,2] => 3 [5,2,1,1] => 5 [5,1,1,1,1] => 5 [4,4,1] => 3 [4,3,2] => 4 [4,3,1,1] => 5 [4,2,2,1] => 5 [4,2,1,1,1] => 5 [4,1,1,1,1,1] => 5 [3,3,3] => 2 [3,3,2,1] => 5 [3,3,1,1,1] => 5 [3,2,2,2] => 4 [3,2,2,1,1] => 5 [3,2,1,1,1,1] => 5 [3,1,1,1,1,1,1] => 5 [2,2,2,2,1] => 5 [2,2,2,1,1,1] => 5 [2,2,1,1,1,1,1] => 5 [2,1,1,1,1,1,1,1] => 5 [1,1,1,1,1,1,1,1,1] => 5 [10] => 0 [9,1] => 2 [8,2] => 0 [8,1,1] => 2 [7,3] => 2 [7,2,1] => 4 [7,1,1,1] => 4 [6,4] => 0 [6,3,1] => 4 [6,2,2] => 0 [6,2,1,1] => 4 [6,1,1,1,1] => 4 [5,5] => 1 [5,4,1] => 3 [5,3,2] => 3 [5,3,1,1] => 5 [5,2,2,1] => 5 [5,2,1,1,1] => 5 [5,1,1,1,1,1] => 5 [4,4,2] => 0 [4,4,1,1] => 3 [4,3,3] => 2 [4,3,2,1] => 5 [4,3,1,1,1] => 5 [4,2,2,2] => 0 [4,2,2,1,1] => 5 [4,2,1,1,1,1] => 5 [4,1,1,1,1,1,1] => 5 [3,3,3,1] => 4 [3,3,2,2] => 3 [3,3,2,1,1] => 5 [3,3,1,1,1,1] => 5 [3,2,2,2,1] => 5 [3,2,2,1,1,1] => 5 [3,2,1,1,1,1,1] => 5 [3,1,1,1,1,1,1,1] => 5 [2,2,2,2,2] => 0 [2,2,2,2,1,1] => 5 [2,2,2,1,1,1,1] => 5 [2,2,1,1,1,1,1,1] => 5 [2,1,1,1,1,1,1,1,1] => 5 [1,1,1,1,1,1,1,1,1,1] => 5 [11] => 1 [10,1] => 2 [9,2] => 2 [9,1,1] => 3 [8,3] => 2 [8,2,1] => 4 [8,1,1,1] => 4 [7,4] => 2 [7,3,1] => 4 [7,2,2] => 3 [7,2,1,1] => 5 [7,1,1,1,1] => 5 [6,5] => 2 [6,4,1] => 4 [6,3,2] => 4 [6,3,1,1] => 6 [6,2,2,1] => 6 [6,2,1,1,1] => 6 [6,1,1,1,1,1] => 6 [5,5,1] => 3 [5,4,2] => 4 [5,4,1,1] => 5 [5,3,3] => 3 [5,3,2,1] => 6 [5,3,1,1,1] => 6 [5,2,2,2] => 4 [5,2,2,1,1] => 6 [5,2,1,1,1,1] => 6 [5,1,1,1,1,1,1] => 6 [4,4,3] => 3 [4,4,2,1] => 6 [4,4,1,1,1] => 6 [4,3,3,1] => 5 [4,3,2,2] => 5 [4,3,2,1,1] => 6 [4,3,1,1,1,1] => 6 [4,2,2,2,1] => 6 [4,2,2,1,1,1] => 6 [4,2,1,1,1,1,1] => 6 [4,1,1,1,1,1,1,1] => 6 [3,3,3,2] => 4 [3,3,3,1,1] => 6 [3,3,2,2,1] => 6 [3,3,2,1,1,1] => 6 [3,3,1,1,1,1,1] => 6 [3,2,2,2,2] => 5 [3,2,2,2,1,1] => 6 [3,2,2,1,1,1,1] => 6 [3,2,1,1,1,1,1,1] => 6 [3,1,1,1,1,1,1,1,1] => 6 [2,2,2,2,2,1] => 6 [2,2,2,2,1,1,1] => 6 [2,2,2,1,1,1,1,1] => 6 [2,2,1,1,1,1,1,1,1] => 6 [2,1,1,1,1,1,1,1,1,1] => 6 [1,1,1,1,1,1,1,1,1,1,1] => 6 [12] => 0 [11,1] => 2 [10,2] => 0 [10,1,1] => 2 [9,3] => 2 [9,2,1] => 4 [9,1,1,1] => 4 [8,4] => 0 [8,3,1] => 4 [8,2,2] => 0 [8,2,1,1] => 4 [8,1,1,1,1] => 4 [7,5] => 2 [7,4,1] => 4 [7,3,2] => 4 [7,3,1,1] => 6 [7,2,2,1] => 6 [7,2,1,1,1] => 6 [7,1,1,1,1,1] => 6 [6,6] => 0 [6,5,1] => 4 [6,4,2] => 0 [6,4,1,1] => 4 [6,3,3] => 2 [6,3,2,1] => 6 [6,3,1,1,1] => 6 [6,2,2,2] => 0 [6,2,2,1,1] => 6 [6,2,1,1,1,1] => 6 [6,1,1,1,1,1,1] => 6 [5,5,2] => 2 [5,5,1,1] => 4 [5,4,3] => 4 [5,4,2,1] => 6 [5,4,1,1,1] => 6 [5,3,3,1] => 6 [5,3,2,2] => 4 [5,3,2,1,1] => 6 [5,3,1,1,1,1] => 6 [5,2,2,2,1] => 6 [5,2,2,1,1,1] => 6 [5,2,1,1,1,1,1] => 6 [5,1,1,1,1,1,1,1] => 6 [4,4,4] => 0 [4,4,3,1] => 6 [4,4,2,2] => 0 [4,4,2,1,1] => 6 [4,4,1,1,1,1] => 6 [4,3,3,2] => 4 [4,3,3,1,1] => 6 [4,3,2,2,1] => 6 [4,3,2,1,1,1] => 6 [4,3,1,1,1,1,1] => 6 [4,2,2,2,2] => 0 [4,2,2,2,1,1] => 6 [4,2,2,1,1,1,1] => 6 [4,2,1,1,1,1,1,1] => 6 [4,1,1,1,1,1,1,1,1] => 6 [3,3,3,3] => 2 [3,3,3,2,1] => 6 [3,3,3,1,1,1] => 6 [3,3,2,2,2] => 4 [3,3,2,2,1,1] => 6 [3,3,2,1,1,1,1] => 6 [3,3,1,1,1,1,1,1] => 6 [3,2,2,2,2,1] => 6 [3,2,2,2,1,1,1] => 6 [3,2,2,1,1,1,1,1] => 6 [3,2,1,1,1,1,1,1,1] => 6 [3,1,1,1,1,1,1,1,1,1] => 6 [2,2,2,2,2,2] => 0 [2,2,2,2,2,1,1] => 6 [2,2,2,2,1,1,1,1] => 6 [2,2,2,1,1,1,1,1,1] => 6 [2,2,1,1,1,1,1,1,1,1] => 6 [2,1,1,1,1,1,1,1,1,1,1] => 6 [1,1,1,1,1,1,1,1,1,1,1,1] => 6 ----------------------------------------------------------------------------- Created: Jul 16, 2016 at 16:42 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Jul 16, 2016 at 16:42 by Christian Stump