***************************************************************************** * 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: St000075 ----------------------------------------------------------------------------- Collection: Standard tableaux ----------------------------------------------------------------------------- Description: The orbit size of a standard tableau under promotion. ----------------------------------------------------------------------------- References: [1] Schützenberger, M. P. Promotion des morphismes d'ensembles ordonnés [[MathSciNet:0299539]] [2] Stanley, R. P. Promotion and evacuation [[MathSciNet:2515772]] ----------------------------------------------------------------------------- Code: def statistic(self): n = self.size() -1 new = self.promotion(n) i = 1 while new != self: new = new.promotion(n) i = i+1 else: return i ----------------------------------------------------------------------------- Statistic values: [[1]] => 1 [[1,2]] => 1 [[1],[2]] => 1 [[1,2,3]] => 1 [[1,3],[2]] => 2 [[1,2],[3]] => 2 [[1],[2],[3]] => 1 [[1,2,3,4]] => 1 [[1,3,4],[2]] => 3 [[1,2,4],[3]] => 3 [[1,2,3],[4]] => 3 [[1,3],[2,4]] => 2 [[1,2],[3,4]] => 2 [[1,4],[2],[3]] => 3 [[1,3],[2],[4]] => 3 [[1,2],[3],[4]] => 3 [[1],[2],[3],[4]] => 1 [[1,2,3,4,5]] => 1 [[1,3,4,5],[2]] => 4 [[1,2,4,5],[3]] => 4 [[1,2,3,5],[4]] => 4 [[1,2,3,4],[5]] => 4 [[1,3,5],[2,4]] => 2 [[1,2,5],[3,4]] => 3 [[1,3,4],[2,5]] => 3 [[1,2,4],[3,5]] => 2 [[1,2,3],[4,5]] => 3 [[1,4,5],[2],[3]] => 4 [[1,3,5],[2],[4]] => 2 [[1,2,5],[3],[4]] => 4 [[1,3,4],[2],[5]] => 4 [[1,2,4],[3],[5]] => 2 [[1,2,3],[4],[5]] => 4 [[1,4],[2,5],[3]] => 3 [[1,3],[2,5],[4]] => 2 [[1,2],[3,5],[4]] => 3 [[1,3],[2,4],[5]] => 3 [[1,2],[3,4],[5]] => 2 [[1,5],[2],[3],[4]] => 4 [[1,4],[2],[3],[5]] => 4 [[1,3],[2],[4],[5]] => 4 [[1,2],[3],[4],[5]] => 4 [[1],[2],[3],[4],[5]] => 1 [[1,2,3,4,5,6]] => 1 [[1,3,4,5,6],[2]] => 5 [[1,2,4,5,6],[3]] => 5 [[1,2,3,5,6],[4]] => 5 [[1,2,3,4,6],[5]] => 5 [[1,2,3,4,5],[6]] => 5 [[1,3,5,6],[2,4]] => 5 [[1,2,5,6],[3,4]] => 4 [[1,3,4,6],[2,5]] => 5 [[1,2,4,6],[3,5]] => 5 [[1,2,3,6],[4,5]] => 4 [[1,3,4,5],[2,6]] => 4 [[1,2,4,5],[3,6]] => 5 [[1,2,3,5],[4,6]] => 5 [[1,2,3,4],[5,6]] => 4 [[1,4,5,6],[2],[3]] => 5 [[1,3,5,6],[2],[4]] => 5 [[1,2,5,6],[3],[4]] => 5 [[1,3,4,6],[2],[5]] => 5 [[1,2,4,6],[3],[5]] => 5 [[1,2,3,6],[4],[5]] => 5 [[1,3,4,5],[2],[6]] => 5 [[1,2,4,5],[3],[6]] => 5 [[1,2,3,5],[4],[6]] => 5 [[1,2,3,4],[5],[6]] => 5 [[1,3,5],[2,4,6]] => 2 [[1,2,5],[3,4,6]] => 3 [[1,3,4],[2,5,6]] => 3 [[1,2,4],[3,5,6]] => 2 [[1,2,3],[4,5,6]] => 3 [[1,4,6],[2,5],[3]] => 12 [[1,3,6],[2,5],[4]] => 12 [[1,2,6],[3,5],[4]] => 4 [[1,3,6],[2,4],[5]] => 12 [[1,2,6],[3,4],[5]] => 12 [[1,4,5],[2,6],[3]] => 4 [[1,3,5],[2,6],[4]] => 12 [[1,2,5],[3,6],[4]] => 12 [[1,3,4],[2,6],[5]] => 12 [[1,2,4],[3,6],[5]] => 12 [[1,2,3],[4,6],[5]] => 4 [[1,3,5],[2,4],[6]] => 12 [[1,2,5],[3,4],[6]] => 12 [[1,3,4],[2,5],[6]] => 4 [[1,2,4],[3,5],[6]] => 12 [[1,2,3],[4,5],[6]] => 12 [[1,5,6],[2],[3],[4]] => 5 [[1,4,6],[2],[3],[5]] => 5 [[1,3,6],[2],[4],[5]] => 5 [[1,2,6],[3],[4],[5]] => 5 [[1,4,5],[2],[3],[6]] => 5 [[1,3,5],[2],[4],[6]] => 5 [[1,2,5],[3],[4],[6]] => 5 [[1,3,4],[2],[5],[6]] => 5 [[1,2,4],[3],[5],[6]] => 5 [[1,2,3],[4],[5],[6]] => 5 [[1,4],[2,5],[3,6]] => 3 [[1,3],[2,5],[4,6]] => 2 [[1,2],[3,5],[4,6]] => 3 [[1,3],[2,4],[5,6]] => 3 [[1,2],[3,4],[5,6]] => 2 [[1,5],[2,6],[3],[4]] => 4 [[1,4],[2,6],[3],[5]] => 5 [[1,3],[2,6],[4],[5]] => 5 [[1,2],[3,6],[4],[5]] => 4 [[1,4],[2,5],[3],[6]] => 4 [[1,3],[2,5],[4],[6]] => 5 [[1,2],[3,5],[4],[6]] => 5 [[1,3],[2,4],[5],[6]] => 4 [[1,2],[3,4],[5],[6]] => 5 [[1,6],[2],[3],[4],[5]] => 5 [[1,5],[2],[3],[4],[6]] => 5 [[1,4],[2],[3],[5],[6]] => 5 [[1,3],[2],[4],[5],[6]] => 5 [[1,2],[3],[4],[5],[6]] => 5 [[1],[2],[3],[4],[5],[6]] => 1 [[1,2,3,4,5,6,7]] => 1 ----------------------------------------------------------------------------- Created: Jun 11, 2013 at 15:46 by Jessica Striker ----------------------------------------------------------------------------- Last Updated: Oct 16, 2015 at 11:54 by Christian Stump