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Identifier
Mp00022: Cores —to partition⟶ Integer partitions
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]
click to show experimental identities (only identities of compositions of up to three maps are shown)
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.
Properties
surjective
Sage code
def mapping(elt):
    return Partition(elt)
Weight
26
Created
Jan 19, 2020 at 07:28 by FindStatCrew
Updated
Jan 19, 2020 at 07:28 by Martin Rubey