*****************************************************************************
* 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: 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