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Identifier
Mp00021: Cores to bounded partition Integer partitions
Images
=>
Cc0013;cc-rep-0Cc0002;cc-rep-1
([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)=>[2,1] ([2,1,1],3)=>[1,1,1] ([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)=>[2,2] ([3,1,1],3)=>[2,1,1] ([2,2,1,1],3)=>[1,1,1,1] ([4,1],4)=>[3,1] ([2,2],4)=>[2,2] ([3,1,1],4)=>[2,1,1] ([2,1,1,1],4)=>[1,1,1,1] ([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)=>[2,2,1] ([4,2,1,1],3)=>[2,1,1,1] ([3,2,2,1,1],3)=>[1,1,1,1,1] ([5,2],4)=>[3,2] ([4,1,1],4)=>[3,1,1] ([3,2,1],4)=>[2,2,1] ([3,1,1,1],4)=>[2,1,1,1] ([2,2,1,1,1],4)=>[1,1,1,1,1] ([5,1],5)=>[4,1] ([3,2],5)=>[3,2] ([4,1,1],5)=>[3,1,1] ([2,2,1],5)=>[2,2,1] ([3,1,1,1],5)=>[2,1,1,1] ([2,1,1,1,1],5)=>[1,1,1,1,1] ([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)=>[2,2,2] ([5,3,1,1],3)=>[2,2,1,1] ([4,2,2,1,1],3)=>[2,1,1,1,1] ([3,3,2,2,1,1],3)=>[1,1,1,1,1,1] ([6,3],4)=>[3,3] ([5,2,1],4)=>[3,2,1] ([4,1,1,1],4)=>[3,1,1,1] ([4,2,2],4)=>[2,2,2] ([3,3,1,1],4)=>[2,2,1,1] ([3,2,1,1,1],4)=>[2,1,1,1,1] ([2,2,2,1,1,1],4)=>[1,1,1,1,1,1] ([6,2],5)=>[4,2] ([5,1,1],5)=>[4,1,1] ([3,3],5)=>[3,3] ([4,2,1],5)=>[3,2,1] ([4,1,1,1],5)=>[3,1,1,1] ([2,2,2],5)=>[2,2,2] ([3,2,1,1],5)=>[2,2,1,1] ([3,1,1,1,1],5)=>[2,1,1,1,1] ([2,2,1,1,1,1],5)=>[1,1,1,1,1,1] ([6,1],6)=>[5,1] ([4,2],6)=>[4,2] ([5,1,1],6)=>[4,1,1] ([3,3],6)=>[3,3] ([3,2,1],6)=>[3,2,1] ([4,1,1,1],6)=>[3,1,1,1] ([2,2,2],6)=>[2,2,2] ([2,2,1,1],6)=>[2,2,1,1] ([3,1,1,1,1],6)=>[2,1,1,1,1] ([2,1,1,1,1,1],6)=>[1,1,1,1,1,1] ([7,2],6)=>[5,2] ([6,1,1],6)=>[5,1,1] ([4,3],6)=>[4,3] ([5,2,1],6)=>[4,2,1] ([5,1,1,1],6)=>[4,1,1,1] ([3,3,1],6)=>[3,3,1] ([3,2,2],6)=>[3,2,2] ([4,2,1,1],6)=>[3,2,1,1] ([4,1,1,1,1],6)=>[3,1,1,1,1] ([2,2,2,1],6)=>[2,2,2,1] ([3,2,1,1,1],6)=>[2,2,1,1,1] ([3,1,1,1,1,1],6)=>[2,1,1,1,1,1] ([2,2,1,1,1,1,1],6)=>[1,1,1,1,1,1,1]
Description
The (k-1)-bounded partition of a k-core.
Starting with a $k$-core, deleting all cells of hook length greater than or equal to $k$ yields a $(k-1)$-bounded partition [1, Theorem 7], see also [2, Section 1.2].
References
[1] Lapointe, L., Morse, J. Tableaux on $k+1$-cores, reduced words for affine permutations, and $k$-Schur expansions MathSciNet:2167475 arXiv:math/0402320
[2] Lam, T., Lapointe, L., Morse, J., Schilling, A., Shimozono, M., Zabrocki, M. $k$-Schur functions and affine Schubert calculus MathSciNet:3379711 arXiv:1301.3569
Properties
graded, bijective
Sage code
def mapping(elt):
    k_boundary = elt.to_partition().k_boundary(elt.k())
    return Partition(k_boundary.row_lengths())

Created
Jan 19, 2020 at 07:28 by FindStatCrew
Updated
Jan 19, 2020 at 07:28 by Martin Rubey