- FindStat

Identifier

St000256: Integer partitions ⟶ ℤ

Values

=>
                            Cc0002;cc-rep
                            
                            
                            

                        []=>0
[1]=>0
[2]=>1
[1,1]=>0
[3]=>1
[2,1]=>0
[1,1,1]=>0
[4]=>1
[3,1]=>1
[2,2]=>1
[2,1,1]=>0
[1,1,1,1]=>0
[5]=>1
[4,1]=>1
[3,2]=>1
[3,1,1]=>1
[2,2,1]=>0
[2,1,1,1]=>0
[1,1,1,1,1]=>0
[6]=>1
[5,1]=>1
[4,2]=>2
[4,1,1]=>1
[3,3]=>1
[3,2,1]=>0
[3,1,1,1]=>1
[2,2,2]=>1
[2,2,1,1]=>0
[2,1,1,1,1]=>0
[1,1,1,1,1,1]=>0
[7]=>1
[6,1]=>1
[5,2]=>2
[5,1,1]=>1
[4,3]=>1
[4,2,1]=>1
[4,1,1,1]=>1
[3,3,1]=>1
[3,2,2]=>1
[3,2,1,1]=>0
[3,1,1,1,1]=>1
[2,2,2,1]=>0
[2,2,1,1,1]=>0
[2,1,1,1,1,1]=>0
[1,1,1,1,1,1,1]=>0
[8]=>1
[7,1]=>1
[6,2]=>2
[6,1,1]=>1
[5,3]=>2
[5,2,1]=>1
[5,1,1,1]=>1
[4,4]=>1
[4,3,1]=>1
[4,2,2]=>2
[4,2,1,1]=>1
[4,1,1,1,1]=>1
[3,3,2]=>1
[3,3,1,1]=>1
[3,2,2,1]=>0
[3,2,1,1,1]=>0
[3,1,1,1,1,1]=>1
[2,2,2,2]=>1
[2,2,2,1,1]=>0
[2,2,1,1,1,1]=>0
[2,1,1,1,1,1,1]=>0
[1,1,1,1,1,1,1,1]=>0
[9]=>1
[8,1]=>1
[7,2]=>2
[7,1,1]=>1
[6,3]=>2
[6,2,1]=>1
[6,1,1,1]=>1
[5,4]=>1
[5,3,1]=>2
[5,2,2]=>2
[5,2,1,1]=>1
[5,1,1,1,1]=>1
[4,4,1]=>1
[4,3,2]=>1
[4,3,1,1]=>1
[4,2,2,1]=>1
[4,2,1,1,1]=>1
[4,1,1,1,1,1]=>1
[3,3,3]=>1
[3,3,2,1]=>0
[3,3,1,1,1]=>1
[3,2,2,2]=>1
[3,2,2,1,1]=>0
[3,2,1,1,1,1]=>0
[3,1,1,1,1,1,1]=>1
[2,2,2,2,1]=>0
[2,2,2,1,1,1]=>0
[2,2,1,1,1,1,1]=>0
[2,1,1,1,1,1,1,1]=>0
[1,1,1,1,1,1,1,1,1]=>0
[10]=>1
[9,1]=>1
[8,2]=>2
[8,1,1]=>1
[7,3]=>2
[7,2,1]=>1
[7,1,1,1]=>1
[6,4]=>2
[6,3,1]=>2
[6,2,2]=>2
[6,2,1,1]=>1
[6,1,1,1,1]=>1
[5,5]=>1
[5,4,1]=>1
[5,3,2]=>2
[5,3,1,1]=>2
[5,2,2,1]=>1
[5,2,1,1,1]=>1
[5,1,1,1,1,1]=>1
[4,4,2]=>2
[4,4,1,1]=>1
[4,3,3]=>1
[4,3,2,1]=>0
[4,3,1,1,1]=>1
[4,2,2,2]=>2
[4,2,2,1,1]=>1
[4,2,1,1,1,1]=>1
[4,1,1,1,1,1,1]=>1
[3,3,3,1]=>1
[3,3,2,2]=>1
[3,3,2,1,1]=>0
[3,3,1,1,1,1]=>1
[3,2,2,2,1]=>0
[3,2,2,1,1,1]=>0
[3,2,1,1,1,1,1]=>0
[3,1,1,1,1,1,1,1]=>1
[2,2,2,2,2]=>1
[2,2,2,2,1,1]=>0
[2,2,2,1,1,1,1]=>0
[2,2,1,1,1,1,1,1]=>0
[2,1,1,1,1,1,1,1,1]=>0
[1,1,1,1,1,1,1,1,1,1]=>0
                    

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Description

The number of parts from which one can substract 2 and still get an integer partition.

References

[1] Tewari, V. V. Kronecker coefficients for some near-rectangular partitions MathSciNet:3320625 arXiv:1403.5327

Code

def statistic(x):
    x = list(x)+[0]
    return sum( 1 for i in range(len(x)-1) if x[i]-2 >= x[i+1] )

Created

Jul 14, 2015 at 21:39 by Christian Stump

Updated

Oct 29, 2017 at 16:37 by Martin Rubey