***************************************************************************** * 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: St000256 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: The number of parts from which one can substract 2 and still get an integer partition. ----------------------------------------------------------------------------- References: [1] Tewari, V. V. Kronecker coefficients for some near-rectangular partitions [[MathSciNet:3320625]] [[arXiv:1403.5327]] ----------------------------------------------------------------------------- Code: def statistic(x): x = list(x)+[0] return sum( 1 for i in range(len(x)-1) if x[i]-2 >= x[i+1] ) ----------------------------------------------------------------------------- Statistic values: [] => 0 [1] => 0 [2] => 1 [1,1] => 0 [3] => 1 [2,1] => 0 [1,1,1] => 0 [4] => 1 [3,1] => 1 [2,2] => 1 [2,1,1] => 0 [1,1,1,1] => 0 [5] => 1 [4,1] => 1 [3,2] => 1 [3,1,1] => 1 [2,2,1] => 0 [2,1,1,1] => 0 [1,1,1,1,1] => 0 [6] => 1 [5,1] => 1 [4,2] => 2 [4,1,1] => 1 [3,3] => 1 [3,2,1] => 0 [3,1,1,1] => 1 [2,2,2] => 1 [2,2,1,1] => 0 [2,1,1,1,1] => 0 [1,1,1,1,1,1] => 0 [7] => 1 [6,1] => 1 [5,2] => 2 [5,1,1] => 1 [4,3] => 1 [4,2,1] => 1 [4,1,1,1] => 1 [3,3,1] => 1 [3,2,2] => 1 [3,2,1,1] => 0 [3,1,1,1,1] => 1 [2,2,2,1] => 0 [2,2,1,1,1] => 0 [2,1,1,1,1,1] => 0 [1,1,1,1,1,1,1] => 0 [8] => 1 [7,1] => 1 [6,2] => 2 [6,1,1] => 1 [5,3] => 2 [5,2,1] => 1 [5,1,1,1] => 1 [4,4] => 1 [4,3,1] => 1 [4,2,2] => 2 [4,2,1,1] => 1 [4,1,1,1,1] => 1 [3,3,2] => 1 [3,3,1,1] => 1 [3,2,2,1] => 0 [3,2,1,1,1] => 0 [3,1,1,1,1,1] => 1 [2,2,2,2] => 1 [2,2,2,1,1] => 0 [2,2,1,1,1,1] => 0 [2,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1] => 0 [9] => 1 [8,1] => 1 [7,2] => 2 [7,1,1] => 1 [6,3] => 2 [6,2,1] => 1 [6,1,1,1] => 1 [5,4] => 1 [5,3,1] => 2 [5,2,2] => 2 [5,2,1,1] => 1 [5,1,1,1,1] => 1 [4,4,1] => 1 [4,3,2] => 1 [4,3,1,1] => 1 [4,2,2,1] => 1 [4,2,1,1,1] => 1 [4,1,1,1,1,1] => 1 [3,3,3] => 1 [3,3,2,1] => 0 [3,3,1,1,1] => 1 [3,2,2,2] => 1 [3,2,2,1,1] => 0 [3,2,1,1,1,1] => 0 [3,1,1,1,1,1,1] => 1 [2,2,2,2,1] => 0 [2,2,2,1,1,1] => 0 [2,2,1,1,1,1,1] => 0 [2,1,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1,1] => 0 [10] => 1 [9,1] => 1 [8,2] => 2 [8,1,1] => 1 [7,3] => 2 [7,2,1] => 1 [7,1,1,1] => 1 [6,4] => 2 [6,3,1] => 2 [6,2,2] => 2 [6,2,1,1] => 1 [6,1,1,1,1] => 1 [5,5] => 1 [5,4,1] => 1 [5,3,2] => 2 [5,3,1,1] => 2 [5,2,2,1] => 1 [5,2,1,1,1] => 1 [5,1,1,1,1,1] => 1 [4,4,2] => 2 [4,4,1,1] => 1 [4,3,3] => 1 [4,3,2,1] => 0 [4,3,1,1,1] => 1 [4,2,2,2] => 2 [4,2,2,1,1] => 1 [4,2,1,1,1,1] => 1 [4,1,1,1,1,1,1] => 1 [3,3,3,1] => 1 [3,3,2,2] => 1 [3,3,2,1,1] => 0 [3,3,1,1,1,1] => 1 [3,2,2,2,1] => 0 [3,2,2,1,1,1] => 0 [3,2,1,1,1,1,1] => 0 [3,1,1,1,1,1,1,1] => 1 [2,2,2,2,2] => 1 [2,2,2,2,1,1] => 0 [2,2,2,1,1,1,1] => 0 [2,2,1,1,1,1,1,1] => 0 [2,1,1,1,1,1,1,1,1] => 0 [1,1,1,1,1,1,1,1,1,1] => 0 ----------------------------------------------------------------------------- Created: Jul 14, 2015 at 21:39 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Oct 29, 2017 at 16:37 by Martin Rubey