edit this map or download as text // json
Identifier
Mp00022: Cores to 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)=>[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]
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)

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