***************************************************************************** * 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: St001435 ----------------------------------------------------------------------------- Collection: Skew partitions ----------------------------------------------------------------------------- Description: The number of missing boxes in the first row. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(L): rem = L[1] if not rem: return 0 else: return rem[0] ----------------------------------------------------------------------------- Statistic values: [[1],[]] => 0 [[2],[]] => 0 [[1,1],[]] => 0 [[2,1],[1]] => 1 [[3],[]] => 0 [[2,1],[]] => 0 [[3,1],[1]] => 1 [[2,2],[1]] => 1 [[3,2],[2]] => 2 [[1,1,1],[]] => 0 [[2,2,1],[1,1]] => 1 [[2,1,1],[1]] => 1 [[3,2,1],[2,1]] => 2 [[4],[]] => 0 [[3,1],[]] => 0 [[4,1],[1]] => 1 [[2,2],[]] => 0 [[3,2],[1]] => 1 [[4,2],[2]] => 2 [[2,1,1],[]] => 0 [[3,2,1],[1,1]] => 1 [[3,1,1],[1]] => 1 [[4,2,1],[2,1]] => 2 [[3,3],[2]] => 2 [[4,3],[3]] => 3 [[2,2,1],[1]] => 1 [[3,3,1],[2,1]] => 2 [[3,2,1],[2]] => 2 [[4,3,1],[3,1]] => 3 [[2,2,2],[1,1]] => 1 [[3,3,2],[2,2]] => 2 [[3,2,2],[2,1]] => 2 [[4,3,2],[3,2]] => 3 [[1,1,1,1],[]] => 0 [[2,2,2,1],[1,1,1]] => 1 [[2,2,1,1],[1,1]] => 1 [[3,3,2,1],[2,2,1]] => 2 [[2,1,1,1],[1]] => 1 [[3,2,2,1],[2,1,1]] => 2 [[3,2,1,1],[2,1]] => 2 [[4,3,2,1],[3,2,1]] => 3 [[5],[]] => 0 [[4,1],[]] => 0 [[5,1],[1]] => 1 [[3,2],[]] => 0 [[4,2],[1]] => 1 [[5,2],[2]] => 2 [[3,1,1],[]] => 0 [[4,2,1],[1,1]] => 1 [[4,1,1],[1]] => 1 [[5,2,1],[2,1]] => 2 [[3,3],[1]] => 1 [[4,3],[2]] => 2 [[5,3],[3]] => 3 [[2,2,1],[]] => 0 [[3,3,1],[1,1]] => 1 [[3,2,1],[1]] => 1 [[4,3,1],[2,1]] => 2 [[4,2,1],[2]] => 2 [[5,3,1],[3,1]] => 3 [[3,2,2],[1,1]] => 1 [[4,3,2],[2,2]] => 2 [[4,2,2],[2,1]] => 2 [[5,3,2],[3,2]] => 3 [[2,1,1,1],[]] => 0 [[3,2,2,1],[1,1,1]] => 1 [[3,2,1,1],[1,1]] => 1 [[4,3,2,1],[2,2,1]] => 2 [[3,1,1,1],[1]] => 1 [[4,2,2,1],[2,1,1]] => 2 [[4,2,1,1],[2,1]] => 2 [[5,3,2,1],[3,2,1]] => 3 [[4,4],[3]] => 3 [[5,4],[4]] => 4 [[3,3,1],[2]] => 2 [[4,4,1],[3,1]] => 3 [[4,3,1],[3]] => 3 [[5,4,1],[4,1]] => 4 [[2,2,2],[1]] => 1 [[3,3,2],[2,1]] => 2 [[4,4,2],[3,2]] => 3 [[3,2,2],[2]] => 2 [[4,3,2],[3,1]] => 3 [[5,4,2],[4,2]] => 4 [[2,2,1,1],[1]] => 1 [[3,3,2,1],[2,1,1]] => 2 [[3,3,1,1],[2,1]] => 2 [[4,4,2,1],[3,2,1]] => 3 [[3,2,1,1],[2]] => 2 [[4,3,2,1],[3,1,1]] => 3 [[4,3,1,1],[3,1]] => 3 [[5,4,2,1],[4,2,1]] => 4 [[3,3,3],[2,2]] => 2 [[4,4,3],[3,3]] => 3 [[4,3,3],[3,2]] => 3 [[5,4,3],[4,3]] => 4 [[2,2,2,1],[1,1]] => 1 [[3,3,3,1],[2,2,1]] => 2 [[3,3,2,1],[2,2]] => 2 [[4,4,3,1],[3,3,1]] => 3 [[3,2,2,1],[2,1]] => 2 [[4,3,3,1],[3,2,1]] => 3 [[4,3,2,1],[3,2]] => 3 [[5,4,3,1],[4,3,1]] => 4 [[2,2,2,2],[1,1,1]] => 1 [[3,3,3,2],[2,2,2]] => 2 [[3,3,2,2],[2,2,1]] => 2 [[4,4,3,2],[3,3,2]] => 3 [[3,2,2,2],[2,1,1]] => 2 [[4,3,3,2],[3,2,2]] => 3 [[4,3,2,2],[3,2,1]] => 3 [[5,4,3,2],[4,3,2]] => 4 [[1,1,1,1,1],[]] => 0 [[2,2,2,2,1],[1,1,1,1]] => 1 [[2,2,2,1,1],[1,1,1]] => 1 [[3,3,3,2,1],[2,2,2,1]] => 2 [[2,2,1,1,1],[1,1]] => 1 [[3,3,2,2,1],[2,2,1,1]] => 2 [[3,3,2,1,1],[2,2,1]] => 2 [[4,4,3,2,1],[3,3,2,1]] => 3 [[2,1,1,1,1],[1]] => 1 [[3,2,2,2,1],[2,1,1,1]] => 2 [[3,2,2,1,1],[2,1,1]] => 2 [[4,3,3,2,1],[3,2,2,1]] => 3 [[3,2,1,1,1],[2,1]] => 2 [[4,3,2,2,1],[3,2,1,1]] => 3 [[4,3,2,1,1],[3,2,1]] => 3 [[5,4,3,2,1],[4,3,2,1]] => 4 ----------------------------------------------------------------------------- Created: Jun 27, 2019 at 14:15 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Jun 27, 2019 at 14:15 by Christian Stump