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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]
          

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