Identifier
Identifier
Values
[] generating graphics... => 0
[1] generating graphics... => 0
[2] generating graphics... => 0
[1,1] generating graphics... => 1
[3] generating graphics... => 0
[2,1] generating graphics... => 0
[1,1,1] generating graphics... => 1
[4] generating graphics... => 0
[3,1] generating graphics... => 0
[2,2] generating graphics... => 1
[2,1,1] generating graphics... => 1
[1,1,1,1] generating graphics... => 1
[5] generating graphics... => 0
[4,1] generating graphics... => 0
[3,2] generating graphics... => 0
[3,1,1] generating graphics... => 1
[2,2,1] generating graphics... => 1
[2,1,1,1] generating graphics... => 1
[1,1,1,1,1] generating graphics... => 1
[6] generating graphics... => 0
[5,1] generating graphics... => 0
[4,2] generating graphics... => 0
[4,1,1] generating graphics... => 1
[3,3] generating graphics... => 1
[3,2,1] generating graphics... => 0
[3,1,1,1] generating graphics... => 1
[2,2,2] generating graphics... => 1
[2,2,1,1] generating graphics... => 2
[2,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1] generating graphics... => 1
[7] generating graphics... => 0
[6,1] generating graphics... => 0
[5,2] generating graphics... => 0
[5,1,1] generating graphics... => 1
[4,3] generating graphics... => 0
[4,2,1] generating graphics... => 0
[4,1,1,1] generating graphics... => 1
[3,3,1] generating graphics... => 1
[3,2,2] generating graphics... => 1
[3,2,1,1] generating graphics... => 1
[3,1,1,1,1] generating graphics... => 1
[2,2,2,1] generating graphics... => 1
[2,2,1,1,1] generating graphics... => 2
[2,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1] generating graphics... => 1
[8] generating graphics... => 0
[7,1] generating graphics... => 0
[6,2] generating graphics... => 0
[6,1,1] generating graphics... => 1
[5,3] generating graphics... => 0
[5,2,1] generating graphics... => 0
[5,1,1,1] generating graphics... => 1
[4,4] generating graphics... => 1
[4,3,1] generating graphics... => 0
[4,2,2] generating graphics... => 1
[4,2,1,1] generating graphics... => 1
[4,1,1,1,1] generating graphics... => 1
[3,3,2] generating graphics... => 1
[3,3,1,1] generating graphics... => 2
[3,2,2,1] generating graphics... => 1
[3,2,1,1,1] generating graphics... => 1
[3,1,1,1,1,1] generating graphics... => 1
[2,2,2,2] generating graphics... => 1
[2,2,2,1,1] generating graphics... => 2
[2,2,1,1,1,1] generating graphics... => 2
[2,1,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1,1] generating graphics... => 1
[9] generating graphics... => 0
[8,1] generating graphics... => 0
[7,2] generating graphics... => 0
[7,1,1] generating graphics... => 1
[6,3] generating graphics... => 0
[6,2,1] generating graphics... => 0
[6,1,1,1] generating graphics... => 1
[5,4] generating graphics... => 0
[5,3,1] generating graphics... => 0
[5,2,2] generating graphics... => 1
[5,2,1,1] generating graphics... => 1
[5,1,1,1,1] generating graphics... => 1
[4,4,1] generating graphics... => 1
[4,3,2] generating graphics... => 0
[4,3,1,1] generating graphics... => 1
[4,2,2,1] generating graphics... => 1
[4,2,1,1,1] generating graphics... => 1
[4,1,1,1,1,1] generating graphics... => 1
[3,3,3] generating graphics... => 1
[3,3,2,1] generating graphics... => 1
[3,3,1,1,1] generating graphics... => 2
[3,2,2,2] generating graphics... => 1
[3,2,2,1,1] generating graphics... => 2
[3,2,1,1,1,1] generating graphics... => 1
[3,1,1,1,1,1,1] generating graphics... => 1
[2,2,2,2,1] generating graphics... => 1
[2,2,2,1,1,1] generating graphics... => 2
[2,2,1,1,1,1,1] generating graphics... => 2
[2,1,1,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1,1,1] generating graphics... => 1
[10] generating graphics... => 0
[9,1] generating graphics... => 0
[8,2] generating graphics... => 0
[8,1,1] generating graphics... => 1
[7,3] generating graphics... => 0
[7,2,1] generating graphics... => 0
[7,1,1,1] generating graphics... => 1
[6,4] generating graphics... => 0
[6,3,1] generating graphics... => 0
[6,2,2] generating graphics... => 1
[6,2,1,1] generating graphics... => 1
[6,1,1,1,1] generating graphics... => 1
[5,5] generating graphics... => 1
[5,4,1] generating graphics... => 0
[5,3,2] generating graphics... => 0
[5,3,1,1] generating graphics... => 1
[5,2,2,1] generating graphics... => 1
[5,2,1,1,1] generating graphics... => 1
[5,1,1,1,1,1] generating graphics... => 1
[4,4,2] generating graphics... => 1
[4,4,1,1] generating graphics... => 2
[4,3,3] generating graphics... => 1
[4,3,2,1] generating graphics... => 0
[4,3,1,1,1] generating graphics... => 1
[4,2,2,2] generating graphics... => 1
[4,2,2,1,1] generating graphics... => 2
[4,2,1,1,1,1] generating graphics... => 1
[4,1,1,1,1,1,1] generating graphics... => 1
[3,3,3,1] generating graphics... => 1
[3,3,2,2] generating graphics... => 2
[3,3,2,1,1] generating graphics... => 2
[3,3,1,1,1,1] generating graphics... => 2
[3,2,2,2,1] generating graphics... => 1
[3,2,2,1,1,1] generating graphics... => 2
[3,2,1,1,1,1,1] generating graphics... => 1
[3,1,1,1,1,1,1,1] generating graphics... => 1
[2,2,2,2,2] generating graphics... => 1
[2,2,2,2,1,1] generating graphics... => 2
[2,2,2,1,1,1,1] generating graphics... => 2
[2,2,1,1,1,1,1,1] generating graphics... => 2
[2,1,1,1,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[5,4,2] generating graphics... => 0
[5,4,1,1] generating graphics... => 1
[5,3,3] generating graphics... => 1
[5,3,2,1] generating graphics... => 0
[5,3,1,1,1] generating graphics... => 1
[5,2,2,2] generating graphics... => 1
[5,2,2,1,1] generating graphics... => 2
[4,4,3] generating graphics... => 1
[4,4,2,1] generating graphics... => 1
[4,4,1,1,1] generating graphics... => 2
[4,3,3,1] generating graphics... => 1
[4,3,2,2] generating graphics... => 1
[4,3,2,1,1] generating graphics... => 1
[4,2,2,2,1] generating graphics... => 1
[3,3,3,2] generating graphics... => 1
[3,3,3,1,1] generating graphics... => 2
[3,3,2,2,1] generating graphics... => 2
[6,4,2] generating graphics... => 0
[5,4,3] generating graphics... => 0
[5,4,2,1] generating graphics... => 0
[5,4,1,1,1] generating graphics... => 1
[5,3,3,1] generating graphics... => 1
[5,3,2,2] generating graphics... => 1
[5,3,2,1,1] generating graphics... => 1
[5,2,2,2,1] generating graphics... => 1
[4,4,3,1] generating graphics... => 1
[4,4,2,2] generating graphics... => 2
[4,4,2,1,1] generating graphics... => 2
[4,3,3,2] generating graphics... => 1
[4,3,3,1,1] generating graphics... => 2
[4,3,2,2,1] generating graphics... => 1
[3,3,3,2,1] generating graphics... => 1
[3,3,2,2,1,1] generating graphics... => 3
[5,4,3,1] generating graphics... => 0
[5,4,2,2] generating graphics... => 1
[5,4,2,1,1] generating graphics... => 1
[5,3,3,2] generating graphics... => 1
[5,3,3,1,1] generating graphics... => 2
[5,3,2,2,1] generating graphics... => 1
[4,4,3,2] generating graphics... => 1
[4,4,3,1,1] generating graphics... => 2
[4,4,2,2,1] generating graphics... => 2
[4,3,3,2,1] generating graphics... => 1
[5,4,3,2] generating graphics... => 0
[5,4,3,1,1] generating graphics... => 1
[5,4,2,2,1] generating graphics... => 1
[5,3,3,2,1] generating graphics... => 1
[4,4,3,2,1] generating graphics... => 1
[5,4,3,2,1] generating graphics... => 0
click to show generating function       
Description
The number of distinct parts of a partition that occur at least twice.
See Section 3.3.1 of [2].
References
[1] Tewari, V. V. Kronecker coefficients for some near-rectangular partitions MathSciNet:3320625 arXiv:1403.5327
[2] Pak, I. Partition bijections, a survey MathSciNet:2267263
Code
def statistic(x):
    x = list(x)
    return sum( 1 for part in set(x) if x.count(part) > 1 )
Created
Jul 14, 2015 at 21:49 by Christian Stump
Updated
Jan 20, 2018 at 11:51 by Martin Rubey