- FindStat

Identifier

St000225: Integer partitions ⟶ ℤ

Values

=>
                            Cc0002;cc-rep
                            
                            
                            

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

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Description

Difference between largest and smallest parts in a partition.

References

[1] Andrews, G. E., Beck, M., Robbins, N. Partitions with fixed differences between largest and smallest parts arXiv:1406.3374
[2] Triangle read by rows, 0<=k<n: T(n,k) = number of partitions of n such that the differences between greatest and smallest parts are k. OEIS:A097364

Code

def statistic(L):
    return L[0]-L[-1]

Created

Oct 13, 2014 at 14:17 by Matthias Beck

Updated

Jun 05, 2020 at 14:05 by Martin Rubey