- FindStat

Identifier

St000318: Integer partitions ⟶ ℤ (values match St000159The number of distinct parts of the integer partition., St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition.)

Values

=>
                            Cc0002;cc-rep
                            
                            
                            

                        []=>1
[1]=>2
[2]=>2
[1,1]=>2
[3]=>2
[2,1]=>3
[1,1,1]=>2
[4]=>2
[3,1]=>3
[2,2]=>2
[2,1,1]=>3
[1,1,1,1]=>2
[5]=>2
[4,1]=>3
[3,2]=>3
[3,1,1]=>3
[2,2,1]=>3
[2,1,1,1]=>3
[1,1,1,1,1]=>2
[6]=>2
[5,1]=>3
[4,2]=>3
[4,1,1]=>3
[3,3]=>2
[3,2,1]=>4
[3,1,1,1]=>3
[2,2,2]=>2
[2,2,1,1]=>3
[2,1,1,1,1]=>3
[1,1,1,1,1,1]=>2
[7]=>2
[6,1]=>3
[5,2]=>3
[5,1,1]=>3
[4,3]=>3
[4,2,1]=>4
[4,1,1,1]=>3
[3,3,1]=>3
[3,2,2]=>3
[3,2,1,1]=>4
[3,1,1,1,1]=>3
[2,2,2,1]=>3
[2,2,1,1,1]=>3
[2,1,1,1,1,1]=>3
[1,1,1,1,1,1,1]=>2
[8]=>2
[7,1]=>3
[6,2]=>3
[6,1,1]=>3
[5,3]=>3
[5,2,1]=>4
[5,1,1,1]=>3
[4,4]=>2
[4,3,1]=>4
[4,2,2]=>3
[4,2,1,1]=>4
[4,1,1,1,1]=>3
[3,3,2]=>3
[3,3,1,1]=>3
[3,2,2,1]=>4
[3,2,1,1,1]=>4
[3,1,1,1,1,1]=>3
[2,2,2,2]=>2
[2,2,2,1,1]=>3
[2,2,1,1,1,1]=>3
[2,1,1,1,1,1,1]=>3
[1,1,1,1,1,1,1,1]=>2
[9]=>2
[8,1]=>3
[7,2]=>3
[7,1,1]=>3
[6,3]=>3
[6,2,1]=>4
[6,1,1,1]=>3
[5,4]=>3
[5,3,1]=>4
[5,2,2]=>3
[5,2,1,1]=>4
[5,1,1,1,1]=>3
[4,4,1]=>3
[4,3,2]=>4
[4,3,1,1]=>4
[4,2,2,1]=>4
[4,2,1,1,1]=>4
[4,1,1,1,1,1]=>3
[3,3,3]=>2
[3,3,2,1]=>4
[3,3,1,1,1]=>3
[3,2,2,2]=>3
[3,2,2,1,1]=>4
[3,2,1,1,1,1]=>4
[3,1,1,1,1,1,1]=>3
[2,2,2,2,1]=>3
[2,2,2,1,1,1]=>3
[2,2,1,1,1,1,1]=>3
[2,1,1,1,1,1,1,1]=>3
[1,1,1,1,1,1,1,1,1]=>2
[10]=>2
[9,1]=>3
[8,2]=>3
[8,1,1]=>3
[7,3]=>3
[7,2,1]=>4
[7,1,1,1]=>3
[6,4]=>3
[6,3,1]=>4
[6,2,2]=>3
[6,2,1,1]=>4
[6,1,1,1,1]=>3
[5,5]=>2
[5,4,1]=>4
[5,3,2]=>4
[5,3,1,1]=>4
[5,2,2,1]=>4
[5,2,1,1,1]=>4
[5,1,1,1,1,1]=>3
[4,4,2]=>3
[4,4,1,1]=>3
[4,3,3]=>3
[4,3,2,1]=>5
[4,3,1,1,1]=>4
[4,2,2,2]=>3
[4,2,2,1,1]=>4
[4,2,1,1,1,1]=>4
[4,1,1,1,1,1,1]=>3
[3,3,3,1]=>3
[3,3,2,2]=>3
[3,3,2,1,1]=>4
[3,3,1,1,1,1]=>3
[3,2,2,2,1]=>4
[3,2,2,1,1,1]=>4
[3,2,1,1,1,1,1]=>4
[3,1,1,1,1,1,1,1]=>3
[2,2,2,2,2]=>2
[2,2,2,2,1,1]=>3
[2,2,2,1,1,1,1]=>3
[2,2,1,1,1,1,1,1]=>3
[2,1,1,1,1,1,1,1,1]=>3
[1,1,1,1,1,1,1,1,1,1]=>2
[5,4,2]=>4
[5,4,1,1]=>4
[5,3,3]=>3
[5,3,2,1]=>5
[5,3,1,1,1]=>4
[5,2,2,2]=>3
[5,2,2,1,1]=>4
[4,4,3]=>3
[4,4,2,1]=>4
[4,4,1,1,1]=>3
[4,3,3,1]=>4
[4,3,2,2]=>4
[4,3,2,1,1]=>5
[4,2,2,2,1]=>4
[3,3,3,2]=>3
[3,3,3,1,1]=>3
[3,3,2,2,1]=>4
[6,4,2]=>4
[5,4,3]=>4
[5,4,2,1]=>5
[5,4,1,1,1]=>4
[5,3,3,1]=>4
[5,3,2,2]=>4
[5,3,2,1,1]=>5
[5,2,2,2,1]=>4
[4,4,3,1]=>4
[4,4,2,2]=>3
[4,4,2,1,1]=>4
[4,3,3,2]=>4
[4,3,3,1,1]=>4
[4,3,2,2,1]=>5
[3,3,3,2,1]=>4
[3,3,2,2,1,1]=>4
[5,4,3,1]=>5
[5,4,2,2]=>4
[5,4,2,1,1]=>5
[5,3,3,2]=>4
[5,3,3,1,1]=>4
[5,3,2,2,1]=>5
[4,4,3,2]=>4
[4,4,3,1,1]=>4
[4,4,2,2,1]=>4
[4,3,3,2,1]=>5
[5,4,3,2]=>5
[5,4,3,1,1]=>5
[5,4,2,2,1]=>5
[5,3,3,2,1]=>5
[4,4,3,2,1]=>5
[5,4,3,2,1]=>6
                    

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Description

The number of addable cells of the Ferrers diagram of an integer partition.

Code

def statistic(L):
    return len(L.addable_cells())

Created

Dec 08, 2015 at 16:29 by Christian Stump

Updated

May 14, 2018 at 20:50 by Martin Rubey