*****************************************************************************
* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* 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