***************************************************************************** * 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: St000380 ----------------------------------------------------------------------------- Collection: Integer partitions ----------------------------------------------------------------------------- Description: Half the perimeter of the largest rectangle that fits inside the diagram of an integer partition. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(p): if p: return max( p[i]+i+1 for i in range(len(p)) ) return 0 ----------------------------------------------------------------------------- Statistic values: [] => 0 [1] => 2 [2] => 3 [1,1] => 3 [3] => 4 [2,1] => 3 [1,1,1] => 4 [4] => 5 [3,1] => 4 [2,2] => 4 [2,1,1] => 4 [1,1,1,1] => 5 [5] => 6 [4,1] => 5 [3,2] => 4 [3,1,1] => 4 [2,2,1] => 4 [2,1,1,1] => 5 [1,1,1,1,1] => 6 [6] => 7 [5,1] => 6 [4,2] => 5 [4,1,1] => 5 [3,3] => 5 [3,2,1] => 4 [3,1,1,1] => 5 [2,2,2] => 5 [2,2,1,1] => 5 [2,1,1,1,1] => 6 [1,1,1,1,1,1] => 7 [7] => 8 [6,1] => 7 [5,2] => 6 [5,1,1] => 6 [4,3] => 5 [4,2,1] => 5 [4,1,1,1] => 5 [3,3,1] => 5 [3,2,2] => 5 [3,2,1,1] => 5 [3,1,1,1,1] => 6 [2,2,2,1] => 5 [2,2,1,1,1] => 6 [2,1,1,1,1,1] => 7 [1,1,1,1,1,1,1] => 8 [8] => 9 [7,1] => 8 [6,2] => 7 [6,1,1] => 7 [5,3] => 6 [5,2,1] => 6 [5,1,1,1] => 6 [4,4] => 6 [4,3,1] => 5 [4,2,2] => 5 [4,2,1,1] => 5 [4,1,1,1,1] => 6 [3,3,2] => 5 [3,3,1,1] => 5 [3,2,2,1] => 5 [3,2,1,1,1] => 6 [3,1,1,1,1,1] => 7 [2,2,2,2] => 6 [2,2,2,1,1] => 6 [2,2,1,1,1,1] => 7 [2,1,1,1,1,1,1] => 8 [1,1,1,1,1,1,1,1] => 9 [9] => 10 [8,1] => 9 [7,2] => 8 [7,1,1] => 8 [6,3] => 7 [6,2,1] => 7 [6,1,1,1] => 7 [5,4] => 6 [5,3,1] => 6 [5,2,2] => 6 [5,2,1,1] => 6 [5,1,1,1,1] => 6 [4,4,1] => 6 [4,3,2] => 5 [4,3,1,1] => 5 [4,2,2,1] => 5 [4,2,1,1,1] => 6 [4,1,1,1,1,1] => 7 [3,3,3] => 6 [3,3,2,1] => 5 [3,3,1,1,1] => 6 [3,2,2,2] => 6 [3,2,2,1,1] => 6 [3,2,1,1,1,1] => 7 [3,1,1,1,1,1,1] => 8 [2,2,2,2,1] => 6 [2,2,2,1,1,1] => 7 [2,2,1,1,1,1,1] => 8 [2,1,1,1,1,1,1,1] => 9 [1,1,1,1,1,1,1,1,1] => 10 [10] => 11 [9,1] => 10 [8,2] => 9 [8,1,1] => 9 [7,3] => 8 [7,2,1] => 8 [7,1,1,1] => 8 [6,4] => 7 [6,3,1] => 7 [6,2,2] => 7 [6,2,1,1] => 7 [6,1,1,1,1] => 7 [5,5] => 7 [5,4,1] => 6 [5,3,2] => 6 [5,3,1,1] => 6 [5,2,2,1] => 6 [5,2,1,1,1] => 6 [5,1,1,1,1,1] => 7 [4,4,2] => 6 [4,4,1,1] => 6 [4,3,3] => 6 [4,3,2,1] => 5 [4,3,1,1,1] => 6 [4,2,2,2] => 6 [4,2,2,1,1] => 6 [4,2,1,1,1,1] => 7 [4,1,1,1,1,1,1] => 8 [3,3,3,1] => 6 [3,3,2,2] => 6 [3,3,2,1,1] => 6 [3,3,1,1,1,1] => 7 [3,2,2,2,1] => 6 [3,2,2,1,1,1] => 7 [3,2,1,1,1,1,1] => 8 [3,1,1,1,1,1,1,1] => 9 [2,2,2,2,2] => 7 [2,2,2,2,1,1] => 7 [2,2,2,1,1,1,1] => 8 [2,2,1,1,1,1,1,1] => 9 [2,1,1,1,1,1,1,1,1] => 10 [1,1,1,1,1,1,1,1,1,1] => 11 [11] => 12 [10,1] => 11 [9,2] => 10 [9,1,1] => 10 [8,3] => 9 [8,2,1] => 9 [8,1,1,1] => 9 [7,4] => 8 [7,3,1] => 8 [7,2,2] => 8 [7,2,1,1] => 8 [7,1,1,1,1] => 8 [6,5] => 7 [6,4,1] => 7 [6,3,2] => 7 [6,3,1,1] => 7 [6,2,2,1] => 7 [6,2,1,1,1] => 7 [6,1,1,1,1,1] => 7 [5,5,1] => 7 [5,4,2] => 6 [5,4,1,1] => 6 [5,3,3] => 6 [5,3,2,1] => 6 [5,3,1,1,1] => 6 [5,2,2,2] => 6 [5,2,2,1,1] => 6 [5,2,1,1,1,1] => 7 [5,1,1,1,1,1,1] => 8 [4,4,3] => 6 [4,4,2,1] => 6 [4,4,1,1,1] => 6 [4,3,3,1] => 6 [4,3,2,2] => 6 [4,3,2,1,1] => 6 [4,3,1,1,1,1] => 7 [4,2,2,2,1] => 6 [4,2,2,1,1,1] => 7 [4,2,1,1,1,1,1] => 8 [4,1,1,1,1,1,1,1] => 9 [3,3,3,2] => 6 [3,3,3,1,1] => 6 [3,3,2,2,1] => 6 [3,3,2,1,1,1] => 7 [3,3,1,1,1,1,1] => 8 [3,2,2,2,2] => 7 [3,2,2,2,1,1] => 7 [3,2,2,1,1,1,1] => 8 [3,2,1,1,1,1,1,1] => 9 [3,1,1,1,1,1,1,1,1] => 10 [2,2,2,2,2,1] => 7 [2,2,2,2,1,1,1] => 8 [2,2,2,1,1,1,1,1] => 9 [2,2,1,1,1,1,1,1,1] => 10 [2,1,1,1,1,1,1,1,1,1] => 11 [1,1,1,1,1,1,1,1,1,1,1] => 12 [12] => 13 [11,1] => 12 [10,2] => 11 [10,1,1] => 11 [9,3] => 10 [9,2,1] => 10 [9,1,1,1] => 10 [8,4] => 9 [8,3,1] => 9 [8,2,2] => 9 [8,2,1,1] => 9 [8,1,1,1,1] => 9 [7,5] => 8 [7,4,1] => 8 [7,3,2] => 8 [7,3,1,1] => 8 [7,2,2,1] => 8 [7,2,1,1,1] => 8 [7,1,1,1,1,1] => 8 [6,6] => 8 [6,5,1] => 7 [6,4,2] => 7 [6,4,1,1] => 7 [6,3,3] => 7 [6,3,2,1] => 7 [6,3,1,1,1] => 7 [6,2,2,2] => 7 [6,2,2,1,1] => 7 [6,2,1,1,1,1] => 7 [6,1,1,1,1,1,1] => 8 [5,5,2] => 7 [5,5,1,1] => 7 [5,4,3] => 6 [5,4,2,1] => 6 [5,4,1,1,1] => 6 [5,3,3,1] => 6 [5,3,2,2] => 6 [5,3,2,1,1] => 6 [5,3,1,1,1,1] => 7 [5,2,2,2,1] => 6 [5,2,2,1,1,1] => 7 [5,2,1,1,1,1,1] => 8 [5,1,1,1,1,1,1,1] => 9 [4,4,4] => 7 [4,4,3,1] => 6 [4,4,2,2] => 6 [4,4,2,1,1] => 6 [4,4,1,1,1,1] => 7 [4,3,3,2] => 6 [4,3,3,1,1] => 6 [4,3,2,2,1] => 6 [4,3,2,1,1,1] => 7 [4,3,1,1,1,1,1] => 8 [4,2,2,2,2] => 7 [4,2,2,2,1,1] => 7 [4,2,2,1,1,1,1] => 8 [4,2,1,1,1,1,1,1] => 9 [4,1,1,1,1,1,1,1,1] => 10 [3,3,3,3] => 7 [3,3,3,2,1] => 6 [3,3,3,1,1,1] => 7 [3,3,2,2,2] => 7 [3,3,2,2,1,1] => 7 [3,3,2,1,1,1,1] => 8 [3,3,1,1,1,1,1,1] => 9 [3,2,2,2,2,1] => 7 [3,2,2,2,1,1,1] => 8 [3,2,2,1,1,1,1,1] => 9 [3,2,1,1,1,1,1,1,1] => 10 [3,1,1,1,1,1,1,1,1,1] => 11 [2,2,2,2,2,2] => 8 [2,2,2,2,2,1,1] => 8 [2,2,2,2,1,1,1,1] => 9 [2,2,2,1,1,1,1,1,1] => 10 [2,2,1,1,1,1,1,1,1,1] => 11 [2,1,1,1,1,1,1,1,1,1,1] => 12 [1,1,1,1,1,1,1,1,1,1,1,1] => 13 ----------------------------------------------------------------------------- Created: Feb 09, 2016 at 12:26 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Oct 29, 2017 at 21:02 by Martin Rubey