************************************************************************ * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2013 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. * ************************************************************************ ------------------------------------------------------------------------ Map identifier: Mp00022 ------------------------------------------------------------------------ Map name: to partition ------------------------------------------------------------------------ Domain: Cores ------------------------------------------------------------------------ Codomain: Integer partitions ------------------------------------------------------------------------ Description: Considers a core as a partition. This embedding is graded and injective but not surjective on $k$-cores for a given parameter $k$, while it is surjective and neither graded nor injective on the collection of all cores. ------------------------------------------------------------------------ References: ------------------------------------------------------------------------ Code: def mapping(elt): return Partition(elt) ------------------------------------------------------------------------ Map images: ([2],3) => [2] ([1,1],3) => [1,1] ([2],4) => [2] ([1,1],4) => [1,1] ([2],5) => [2] ([1,1],5) => [1,1] ([2],6) => [2] ([1,1],6) => [1,1] ([3,1],3) => [3,1] ([2,1,1],3) => [2,1,1] ([3],4) => [3] ([2,1],4) => [2,1] ([1,1,1],4) => [1,1,1] ([3],5) => [3] ([2,1],5) => [2,1] ([1,1,1],5) => [1,1,1] ([3],6) => [3] ([2,1],6) => [2,1] ([1,1,1],6) => [1,1,1] ([4,2],3) => [4,2] ([3,1,1],3) => [3,1,1] ([2,2,1,1],3) => [2,2,1,1] ([4,1],4) => [4,1] ([2,2],4) => [2,2] ([3,1,1],4) => [3,1,1] ([2,1,1,1],4) => [2,1,1,1] ([4],5) => [4] ([3,1],5) => [3,1] ([2,2],5) => [2,2] ([2,1,1],5) => [2,1,1] ([1,1,1,1],5) => [1,1,1,1] ([4],6) => [4] ([3,1],6) => [3,1] ([2,2],6) => [2,2] ([2,1,1],6) => [2,1,1] ([1,1,1,1],6) => [1,1,1,1] ([5,3,1],3) => [5,3,1] ([4,2,1,1],3) => [4,2,1,1] ([3,2,2,1,1],3) => [3,2,2,1,1] ([5,2],4) => [5,2] ([4,1,1],4) => [4,1,1] ([3,2,1],4) => [3,2,1] ([3,1,1,1],4) => [3,1,1,1] ([2,2,1,1,1],4) => [2,2,1,1,1] ([5,1],5) => [5,1] ([3,2],5) => [3,2] ([4,1,1],5) => [4,1,1] ([2,2,1],5) => [2,2,1] ([3,1,1,1],5) => [3,1,1,1] ([2,1,1,1,1],5) => [2,1,1,1,1] ([5],6) => [5] ([4,1],6) => [4,1] ([3,2],6) => [3,2] ([3,1,1],6) => [3,1,1] ([2,2,1],6) => [2,2,1] ([2,1,1,1],6) => [2,1,1,1] ([1,1,1,1,1],6) => [1,1,1,1,1] ([6,4,2],3) => [6,4,2] ([5,3,1,1],3) => [5,3,1,1] ([4,2,2,1,1],3) => [4,2,2,1,1] ([3,3,2,2,1,1],3) => [3,3,2,2,1,1] ([6,3],4) => [6,3] ([5,2,1],4) => [5,2,1] ([4,1,1,1],4) => [4,1,1,1] ([4,2,2],4) => [4,2,2] ([3,3,1,1],4) => [3,3,1,1] ([3,2,1,1,1],4) => [3,2,1,1,1] ([2,2,2,1,1,1],4) => [2,2,2,1,1,1] ([6,2],5) => [6,2] ([5,1,1],5) => [5,1,1] ([3,3],5) => [3,3] ([4,2,1],5) => [4,2,1] ([4,1,1,1],5) => [4,1,1,1] ([2,2,2],5) => [2,2,2] ([3,2,1,1],5) => [3,2,1,1] ([3,1,1,1,1],5) => [3,1,1,1,1] ([2,2,1,1,1,1],5) => [2,2,1,1,1,1] ([6,1],6) => [6,1] ([4,2],6) => [4,2] ([5,1,1],6) => [5,1,1] ([3,3],6) => [3,3] ([3,2,1],6) => [3,2,1] ([4,1,1,1],6) => [4,1,1,1] ([2,2,2],6) => [2,2,2] ([2,2,1,1],6) => [2,2,1,1] ([3,1,1,1,1],6) => [3,1,1,1,1] ([2,1,1,1,1,1],6) => [2,1,1,1,1,1] ([7,2],6) => [7,2] ([6,1,1],6) => [6,1,1] ([4,3],6) => [4,3] ([5,2,1],6) => [5,2,1] ([5,1,1,1],6) => [5,1,1,1] ([3,3,1],6) => [3,3,1] ([3,2,2],6) => [3,2,2] ([4,2,1,1],6) => [4,2,1,1] ([4,1,1,1,1],6) => [4,1,1,1,1] ([2,2,2,1],6) => [2,2,2,1] ([3,2,1,1,1],6) => [3,2,1,1,1] ([3,1,1,1,1,1],6) => [3,1,1,1,1,1] ([2,2,1,1,1,1,1],6) => [2,2,1,1,1,1,1] ----------------------------------------------------------------------------- Created: Jan 19, 2020 at 07:28 by FindStatCrew ----------------------------------------------------------------------------- Last Updated: Jan 19, 2020 at 07:28 by Martin Rubey