***************************************************************************** * 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: St001713 ----------------------------------------------------------------------------- Collection: Gelfand-Tsetlin patterns ----------------------------------------------------------------------------- Description: The difference of the first and last value in the first row of the Gelfand-Tsetlin pattern. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(G): return G[0][0]-G[0][-1] ----------------------------------------------------------------------------- Statistic values: [[1,0],[0]] => 1 [[1,0],[1]] => 1 [[2,0],[0]] => 2 [[2,0],[1]] => 2 [[2,0],[2]] => 2 [[1,1],[1]] => 0 [[3,0],[0]] => 3 [[3,0],[1]] => 3 [[3,0],[2]] => 3 [[3,0],[3]] => 3 [[2,1],[1]] => 1 [[2,1],[2]] => 1 [[4,0],[0]] => 4 [[4,0],[1]] => 4 [[4,0],[2]] => 4 [[4,0],[3]] => 4 [[4,0],[4]] => 4 [[3,1],[1]] => 2 [[3,1],[2]] => 2 [[3,1],[3]] => 2 [[2,2],[2]] => 0 [[5,0],[0]] => 5 [[5,0],[1]] => 5 [[5,0],[2]] => 5 [[5,0],[3]] => 5 [[5,0],[4]] => 5 [[5,0],[5]] => 5 [[4,1],[1]] => 3 [[4,1],[2]] => 3 [[4,1],[3]] => 3 [[4,1],[4]] => 3 [[3,2],[2]] => 1 [[3,2],[3]] => 1 [[1,0,0],[0,0],[0]] => 1 [[1,0,0],[1,0],[0]] => 1 [[1,0,0],[1,0],[1]] => 1 [[2,0,0],[0,0],[0]] => 2 [[2,0,0],[1,0],[0]] => 2 [[2,0,0],[1,0],[1]] => 2 [[2,0,0],[2,0],[0]] => 2 [[2,0,0],[2,0],[1]] => 2 [[2,0,0],[2,0],[2]] => 2 [[1,1,0],[1,0],[0]] => 1 [[1,1,0],[1,0],[1]] => 1 [[1,1,0],[1,1],[1]] => 1 [[3,0,0],[0,0],[0]] => 3 [[3,0,0],[1,0],[0]] => 3 [[3,0,0],[1,0],[1]] => 3 [[3,0,0],[2,0],[0]] => 3 [[3,0,0],[2,0],[1]] => 3 [[3,0,0],[2,0],[2]] => 3 [[3,0,0],[3,0],[0]] => 3 [[3,0,0],[3,0],[1]] => 3 [[3,0,0],[3,0],[2]] => 3 [[3,0,0],[3,0],[3]] => 3 [[2,1,0],[1,0],[0]] => 2 [[2,1,0],[1,0],[1]] => 2 [[2,1,0],[1,1],[1]] => 2 [[2,1,0],[2,0],[0]] => 2 [[2,1,0],[2,0],[1]] => 2 [[2,1,0],[2,0],[2]] => 2 [[2,1,0],[2,1],[1]] => 2 [[2,1,0],[2,1],[2]] => 2 [[1,1,1],[1,1],[1]] => 0 [[4,0,0],[0,0],[0]] => 4 [[4,0,0],[1,0],[0]] => 4 [[4,0,0],[1,0],[1]] => 4 [[4,0,0],[2,0],[0]] => 4 [[4,0,0],[2,0],[1]] => 4 [[4,0,0],[2,0],[2]] => 4 [[4,0,0],[3,0],[0]] => 4 [[4,0,0],[3,0],[1]] => 4 [[4,0,0],[3,0],[2]] => 4 [[4,0,0],[3,0],[3]] => 4 [[4,0,0],[4,0],[0]] => 4 [[4,0,0],[4,0],[1]] => 4 [[4,0,0],[4,0],[2]] => 4 [[4,0,0],[4,0],[3]] => 4 [[4,0,0],[4,0],[4]] => 4 [[3,1,0],[1,0],[0]] => 3 [[3,1,0],[1,0],[1]] => 3 [[3,1,0],[1,1],[1]] => 3 [[3,1,0],[2,0],[0]] => 3 [[3,1,0],[2,0],[1]] => 3 [[3,1,0],[2,0],[2]] => 3 [[3,1,0],[2,1],[1]] => 3 [[3,1,0],[2,1],[2]] => 3 [[3,1,0],[3,0],[0]] => 3 [[3,1,0],[3,0],[1]] => 3 [[3,1,0],[3,0],[2]] => 3 [[3,1,0],[3,0],[3]] => 3 [[3,1,0],[3,1],[1]] => 3 [[3,1,0],[3,1],[2]] => 3 [[3,1,0],[3,1],[3]] => 3 [[2,2,0],[2,0],[0]] => 2 [[2,2,0],[2,0],[1]] => 2 [[2,2,0],[2,0],[2]] => 2 [[2,2,0],[2,1],[1]] => 2 [[2,2,0],[2,1],[2]] => 2 [[2,2,0],[2,2],[2]] => 2 [[2,1,1],[1,1],[1]] => 1 [[2,1,1],[2,1],[1]] => 1 [[2,1,1],[2,1],[2]] => 1 [[1,0,0,0],[0,0,0],[0,0],[0]] => 1 [[1,0,0,0],[1,0,0],[0,0],[0]] => 1 [[1,0,0,0],[1,0,0],[1,0],[0]] => 1 [[1,0,0,0],[1,0,0],[1,0],[1]] => 1 [[2,0,0,0],[0,0,0],[0,0],[0]] => 2 [[2,0,0,0],[1,0,0],[0,0],[0]] => 2 [[2,0,0,0],[1,0,0],[1,0],[0]] => 2 [[2,0,0,0],[1,0,0],[1,0],[1]] => 2 [[2,0,0,0],[2,0,0],[0,0],[0]] => 2 [[2,0,0,0],[2,0,0],[1,0],[0]] => 2 [[2,0,0,0],[2,0,0],[1,0],[1]] => 2 [[2,0,0,0],[2,0,0],[2,0],[0]] => 2 [[2,0,0,0],[2,0,0],[2,0],[1]] => 2 [[2,0,0,0],[2,0,0],[2,0],[2]] => 2 [[1,1,0,0],[1,0,0],[0,0],[0]] => 1 [[1,1,0,0],[1,0,0],[1,0],[0]] => 1 [[1,1,0,0],[1,0,0],[1,0],[1]] => 1 [[1,1,0,0],[1,1,0],[1,0],[0]] => 1 [[1,1,0,0],[1,1,0],[1,0],[1]] => 1 [[1,1,0,0],[1,1,0],[1,1],[1]] => 1 [[3,0,0,0],[0,0,0],[0,0],[0]] => 3 [[3,0,0,0],[1,0,0],[0,0],[0]] => 3 [[3,0,0,0],[1,0,0],[1,0],[0]] => 3 [[3,0,0,0],[1,0,0],[1,0],[1]] => 3 [[3,0,0,0],[2,0,0],[0,0],[0]] => 3 [[3,0,0,0],[2,0,0],[1,0],[0]] => 3 [[3,0,0,0],[2,0,0],[1,0],[1]] => 3 [[3,0,0,0],[2,0,0],[2,0],[0]] => 3 [[3,0,0,0],[2,0,0],[2,0],[1]] => 3 [[3,0,0,0],[2,0,0],[2,0],[2]] => 3 [[3,0,0,0],[3,0,0],[0,0],[0]] => 3 [[3,0,0,0],[3,0,0],[1,0],[0]] => 3 [[3,0,0,0],[3,0,0],[1,0],[1]] => 3 [[3,0,0,0],[3,0,0],[2,0],[0]] => 3 [[3,0,0,0],[3,0,0],[2,0],[1]] => 3 [[3,0,0,0],[3,0,0],[2,0],[2]] => 3 [[3,0,0,0],[3,0,0],[3,0],[0]] => 3 [[3,0,0,0],[3,0,0],[3,0],[1]] => 3 [[3,0,0,0],[3,0,0],[3,0],[2]] => 3 [[3,0,0,0],[3,0,0],[3,0],[3]] => 3 [[2,1,0,0],[1,0,0],[0,0],[0]] => 2 [[2,1,0,0],[1,0,0],[1,0],[0]] => 2 [[2,1,0,0],[1,0,0],[1,0],[1]] => 2 [[2,1,0,0],[1,1,0],[1,0],[0]] => 2 [[2,1,0,0],[1,1,0],[1,0],[1]] => 2 [[2,1,0,0],[1,1,0],[1,1],[1]] => 2 [[2,1,0,0],[2,0,0],[0,0],[0]] => 2 [[2,1,0,0],[2,0,0],[1,0],[0]] => 2 [[2,1,0,0],[2,0,0],[1,0],[1]] => 2 [[2,1,0,0],[2,0,0],[2,0],[0]] => 2 [[2,1,0,0],[2,0,0],[2,0],[1]] => 2 [[2,1,0,0],[2,0,0],[2,0],[2]] => 2 [[2,1,0,0],[2,1,0],[1,0],[0]] => 2 [[2,1,0,0],[2,1,0],[1,0],[1]] => 2 [[2,1,0,0],[2,1,0],[1,1],[1]] => 2 [[2,1,0,0],[2,1,0],[2,0],[0]] => 2 [[2,1,0,0],[2,1,0],[2,0],[1]] => 2 [[2,1,0,0],[2,1,0],[2,0],[2]] => 2 [[2,1,0,0],[2,1,0],[2,1],[1]] => 2 [[2,1,0,0],[2,1,0],[2,1],[2]] => 2 [[1,1,1,0],[1,1,0],[1,0],[0]] => 1 [[1,1,1,0],[1,1,0],[1,0],[1]] => 1 [[1,1,1,0],[1,1,0],[1,1],[1]] => 1 [[1,1,1,0],[1,1,1],[1,1],[1]] => 1 [[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 1 [[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 1 [[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 1 [[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 1 [[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 1 [[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 2 [[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 2 [[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 2 [[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 2 [[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 2 [[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => 2 [[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => 2 [[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => 2 [[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => 2 [[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => 2 [[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => 2 [[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => 2 [[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => 2 [[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => 2 [[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => 2 [[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 1 [[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 1 [[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 1 [[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 1 [[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => 1 [[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => 1 [[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => 1 [[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => 1 [[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => 1 [[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => 1 [[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 1 [[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 1 [[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 1 [[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 1 [[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 1 [[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 1 ----------------------------------------------------------------------------- Created: Apr 15, 2021 at 14:50 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Apr 15, 2021 at 14:50 by Martin Rubey