Identifier
Identifier
Values
[1] generating graphics... => 0
[2] generating graphics... => 1
[1,1] generating graphics... => -1
[3] generating graphics... => 2
[2,1] generating graphics... => 0
[1,1,1] generating graphics... => -2
[4] generating graphics... => 3
[3,1] generating graphics... => 1
[2,2] generating graphics... => 0
[2,1,1] generating graphics... => -1
[1,1,1,1] generating graphics... => -3
[5] generating graphics... => 4
[4,1] generating graphics... => 2
[3,2] generating graphics... => 1
[3,1,1] generating graphics... => 0
[2,2,1] generating graphics... => -1
[2,1,1,1] generating graphics... => -2
[1,1,1,1,1] generating graphics... => -4
[6] generating graphics... => 5
[5,1] generating graphics... => 3
[4,2] generating graphics... => 2
[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... => -3
[1,1,1,1,1,1] generating graphics... => -5
[7] generating graphics... => 6
[6,1] generating graphics... => 4
[5,2] generating graphics... => 3
[5,1,1] generating graphics... => 2
[4,3] generating graphics... => 2
[4,2,1] generating graphics... => 1
[4,1,1,1] generating graphics... => 0
[3,3,1] generating graphics... => 0
[3,2,2] generating graphics... => 0
[3,2,1,1] generating graphics... => -1
[3,1,1,1,1] generating graphics... => -2
[2,2,2,1] generating graphics... => -2
[2,2,1,1,1] generating graphics... => -3
[2,1,1,1,1,1] generating graphics... => -4
[1,1,1,1,1,1,1] generating graphics... => -6
[8] generating graphics... => 7
[7,1] generating graphics... => 5
[6,2] generating graphics... => 4
[6,1,1] generating graphics... => 3
[5,3] generating graphics... => 3
[5,2,1] generating graphics... => 2
[5,1,1,1] generating graphics... => 1
[4,4] generating graphics... => 2
[4,3,1] generating graphics... => 1
[4,2,2] generating graphics... => 1
[4,2,1,1] generating graphics... => 0
[4,1,1,1,1] generating graphics... => -1
[3,3,2] generating graphics... => 0
[3,3,1,1] generating graphics... => -1
[3,2,2,1] generating graphics... => -1
[3,2,1,1,1] generating graphics... => -2
[3,1,1,1,1,1] generating graphics... => -3
[2,2,2,2] generating graphics... => -2
[2,2,2,1,1] generating graphics... => -3
[2,2,1,1,1,1] generating graphics... => -4
[2,1,1,1,1,1,1] generating graphics... => -5
[1,1,1,1,1,1,1,1] generating graphics... => -7
[9] generating graphics... => 8
[8,1] generating graphics... => 6
[7,2] generating graphics... => 5
[7,1,1] generating graphics... => 4
[6,3] generating graphics... => 4
[6,2,1] generating graphics... => 3
[6,1,1,1] generating graphics... => 2
[5,4] generating graphics... => 3
[5,3,1] generating graphics... => 2
[5,2,2] generating graphics... => 2
[5,2,1,1] generating graphics... => 1
[5,1,1,1,1] generating graphics... => 0
[4,4,1] generating graphics... => 1
[4,3,2] generating graphics... => 1
[4,3,1,1] generating graphics... => 0
[4,2,2,1] generating graphics... => 0
[4,2,1,1,1] generating graphics... => -1
[4,1,1,1,1,1] generating graphics... => -2
[3,3,3] generating graphics... => 0
[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... => -3
[3,1,1,1,1,1,1] generating graphics... => -4
[2,2,2,2,1] generating graphics... => -3
[2,2,2,1,1,1] generating graphics... => -4
[2,2,1,1,1,1,1] generating graphics... => -5
[2,1,1,1,1,1,1,1] generating graphics... => -6
[1,1,1,1,1,1,1,1,1] generating graphics... => -8
[10] generating graphics... => 9
[9,1] generating graphics... => 7
[8,2] generating graphics... => 6
[8,1,1] generating graphics... => 5
[7,3] generating graphics... => 5
[7,2,1] generating graphics... => 4
[7,1,1,1] generating graphics... => 3
[6,4] generating graphics... => 4
[6,3,1] generating graphics... => 3
[6,2,2] generating graphics... => 3
[6,2,1,1] generating graphics... => 2
[6,1,1,1,1] generating graphics... => 1
[5,5] generating graphics... => 3
[5,4,1] generating graphics... => 2
[5,3,2] generating graphics... => 2
[5,3,1,1] generating graphics... => 1
[5,2,2,1] generating graphics... => 1
[5,2,1,1,1] generating graphics... => 0
[5,1,1,1,1,1] generating graphics... => -1
[4,4,2] generating graphics... => 1
[4,4,1,1] generating graphics... => 0
[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... => 0
[4,2,2,1,1] generating graphics... => -1
[4,2,1,1,1,1] generating graphics... => -2
[4,1,1,1,1,1,1] generating graphics... => -3
[3,3,3,1] generating graphics... => -1
[3,3,2,2] generating graphics... => -1
[3,3,2,1,1] generating graphics... => -2
[3,3,1,1,1,1] generating graphics... => -3
[3,2,2,2,1] generating graphics... => -2
[3,2,2,1,1,1] generating graphics... => -3
[3,2,1,1,1,1,1] generating graphics... => -4
[3,1,1,1,1,1,1,1] generating graphics... => -5
[2,2,2,2,2] generating graphics... => -3
[2,2,2,2,1,1] generating graphics... => -4
[2,2,2,1,1,1,1] generating graphics... => -5
[2,2,1,1,1,1,1,1] generating graphics... => -6
[2,1,1,1,1,1,1,1,1] generating graphics... => -7
[1,1,1,1,1,1,1,1,1,1] generating graphics... => -9
click to show generating function       
Description
The Dyson rank of a partition.
This rank is defined as the largest part minus the number of parts. It was introduced by Dyson [1] in connection to Ramanujan's partition congruences $$p(5n+4) \equiv 0 \pmod 5$$ and $$p(7n+6) \equiv 0 \pmod 7.$$
References
[1] Dyson, F. J. Some guesses in the theory of partitions MathSciNet:3077150
Code
def statistic(L):
    return L[0] - len(L)
Created
Jul 03, 2013 at 14:34 by Olivier Mallet
Updated
May 29, 2015 at 16:57 by Martin Rubey