- FindStat

Identifier

St001568: Integer partitions ⟶ ℤ

Values

=>
                            Cc0002;cc-rep
                            
                            
                            

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

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Description

The smallest positive integer that does not appear twice in the partition.

References

[1] Ballantine, C., Merca, M. Combinatorial Proof of the Minimal Excludant Theorem arXiv:1908.06789

Code

def statistic(x):
    x = list(x)
    for i in range(1, x[0]+2):
        if x.count(i) < 2:
            return i

Created

Jul 15, 2020 at 15:01 by Martin Rubey

Updated

Jul 15, 2020 at 15:01 by Martin Rubey