***************************************************************************** * 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: St000150 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The floored half-sum of the multiplicities of a partition. This statistic is equidistributed with [[St000143]] and [[St000149]], see [1]. ----------------------------------------------------------------------------- References: [1] Tim Statistics on partitions equidistributed with number of even parts [[MathOverflow:134577]] ----------------------------------------------------------------------------- Code: def statistic(L): E = L.to_exp() return sum( floor( e/2 ) for e in E ) ----------------------------------------------------------------------------- Statistic values: [] => 0 [1] => 0 [2] => 0 [1,1] => 1 [3] => 0 [2,1] => 0 [1,1,1] => 1 [4] => 0 [3,1] => 0 [2,2] => 1 [2,1,1] => 1 [1,1,1,1] => 2 [5] => 0 [4,1] => 0 [3,2] => 0 [3,1,1] => 1 [2,2,1] => 1 [2,1,1,1] => 1 [1,1,1,1,1] => 2 [6] => 0 [5,1] => 0 [4,2] => 0 [4,1,1] => 1 [3,3] => 1 [3,2,1] => 0 [3,1,1,1] => 1 [2,2,2] => 1 [2,2,1,1] => 2 [2,1,1,1,1] => 2 [1,1,1,1,1,1] => 3 [7] => 0 [6,1] => 0 [5,2] => 0 [5,1,1] => 1 [4,3] => 0 [4,2,1] => 0 [4,1,1,1] => 1 [3,3,1] => 1 [3,2,2] => 1 [3,2,1,1] => 1 [3,1,1,1,1] => 2 [2,2,2,1] => 1 [2,2,1,1,1] => 2 [2,1,1,1,1,1] => 2 [1,1,1,1,1,1,1] => 3 [8] => 0 [7,1] => 0 [6,2] => 0 [6,1,1] => 1 [5,3] => 0 [5,2,1] => 0 [5,1,1,1] => 1 [4,4] => 1 [4,3,1] => 0 [4,2,2] => 1 [4,2,1,1] => 1 [4,1,1,1,1] => 2 [3,3,2] => 1 [3,3,1,1] => 2 [3,2,2,1] => 1 [3,2,1,1,1] => 1 [3,1,1,1,1,1] => 2 [2,2,2,2] => 2 [2,2,2,1,1] => 2 [2,2,1,1,1,1] => 3 [2,1,1,1,1,1,1] => 3 [1,1,1,1,1,1,1,1] => 4 [9] => 0 [8,1] => 0 [7,2] => 0 [7,1,1] => 1 [6,3] => 0 [6,2,1] => 0 [6,1,1,1] => 1 [5,4] => 0 [5,3,1] => 0 [5,2,2] => 1 [5,2,1,1] => 1 [5,1,1,1,1] => 2 [4,4,1] => 1 [4,3,2] => 0 [4,3,1,1] => 1 [4,2,2,1] => 1 [4,2,1,1,1] => 1 [4,1,1,1,1,1] => 2 [3,3,3] => 1 [3,3,2,1] => 1 [3,3,1,1,1] => 2 [3,2,2,2] => 1 [3,2,2,1,1] => 2 [3,2,1,1,1,1] => 2 [3,1,1,1,1,1,1] => 3 [2,2,2,2,1] => 2 [2,2,2,1,1,1] => 2 [2,2,1,1,1,1,1] => 3 [2,1,1,1,1,1,1,1] => 3 [1,1,1,1,1,1,1,1,1] => 4 [10] => 0 [9,1] => 0 [8,2] => 0 [8,1,1] => 1 [7,3] => 0 [7,2,1] => 0 [7,1,1,1] => 1 [6,4] => 0 [6,3,1] => 0 [6,2,2] => 1 [6,2,1,1] => 1 [6,1,1,1,1] => 2 [5,5] => 1 [5,4,1] => 0 [5,3,2] => 0 [5,3,1,1] => 1 [5,2,2,1] => 1 [5,2,1,1,1] => 1 [5,1,1,1,1,1] => 2 [4,4,2] => 1 [4,4,1,1] => 2 [4,3,3] => 1 [4,3,2,1] => 0 [4,3,1,1,1] => 1 [4,2,2,2] => 1 [4,2,2,1,1] => 2 [4,2,1,1,1,1] => 2 [4,1,1,1,1,1,1] => 3 [3,3,3,1] => 1 [3,3,2,2] => 2 [3,3,2,1,1] => 2 [3,3,1,1,1,1] => 3 [3,2,2,2,1] => 1 [3,2,2,1,1,1] => 2 [3,2,1,1,1,1,1] => 2 [3,1,1,1,1,1,1,1] => 3 [2,2,2,2,2] => 2 [2,2,2,2,1,1] => 3 [2,2,2,1,1,1,1] => 3 [2,2,1,1,1,1,1,1] => 4 [2,1,1,1,1,1,1,1,1] => 4 [1,1,1,1,1,1,1,1,1,1] => 5 [5,4,2] => 0 [5,4,1,1] => 1 [5,3,3] => 1 [5,3,2,1] => 0 [5,3,1,1,1] => 1 [5,2,2,2] => 1 [5,2,2,1,1] => 2 [4,4,3] => 1 [4,4,2,1] => 1 [4,4,1,1,1] => 2 [4,3,3,1] => 1 [4,3,2,2] => 1 [4,3,2,1,1] => 1 [4,2,2,2,1] => 1 [3,3,3,2] => 1 [3,3,3,1,1] => 2 [3,3,2,2,1] => 2 [6,4,2] => 0 [5,4,3] => 0 [5,4,2,1] => 0 [5,4,1,1,1] => 1 [5,3,3,1] => 1 [5,3,2,2] => 1 [5,3,2,1,1] => 1 [5,2,2,2,1] => 1 [4,4,3,1] => 1 [4,4,2,2] => 2 [4,4,2,1,1] => 2 [4,3,3,2] => 1 [4,3,3,1,1] => 2 [4,3,2,2,1] => 1 [3,3,3,2,1] => 1 [3,3,2,2,1,1] => 3 [5,4,3,1] => 0 [5,4,2,2] => 1 [5,4,2,1,1] => 1 [5,3,3,2] => 1 [5,3,3,1,1] => 2 [5,3,2,2,1] => 1 [4,4,3,2] => 1 [4,4,3,1,1] => 2 [4,4,2,2,1] => 2 [4,3,3,2,1] => 1 [5,4,3,2] => 0 [5,4,3,1,1] => 1 [5,4,2,2,1] => 1 [5,3,3,2,1] => 1 [4,4,3,2,1] => 1 [5,4,3,2,1] => 0 [7,5,3,1] => 0 [7,5,4,3,1] => 0 [6,5,4,3,2,1] => 0 [11,7,5,1] => 0 [9,7,5,3,1] => 0 [7,6,5,4,3,2,1] => 0 [9,7,5,5,3,1] => 1 [11,9,7,5,3,1] => 0 [11,8,7,5,4,1] => 0 [8,7,6,5,4,3,2,1] => 0 [11,9,7,6,5,3,1] => 0 [13,11,9,7,5,3,1] => 0 [13,11,9,7,7,5,3,1] => 1 [17,13,11,9,7,5,1] => 0 [15,13,11,9,7,5,3,1] => 0 [29,23,19,17,13,11,7,1] => 0 ----------------------------------------------------------------------------- Created: Jul 08, 2013 at 13:35 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Sep 09, 2020 at 21:28 by Martin Rubey