Identifier
Identifier
Values
[] generating graphics... => 0
[1] generating graphics... => 1
[2] generating graphics... => 2
[1,1] generating graphics... => 1
[3] generating graphics... => 2
[2,1] generating graphics... => 3
[1,1,1] generating graphics... => 1
[4] generating graphics... => 2
[3,1] generating graphics... => 4
[2,2] generating graphics... => 3
[2,1,1] generating graphics... => 2
[1,1,1,1] generating graphics... => 1
[5] generating graphics... => 2
[4,1] generating graphics... => 3
[3,2] generating graphics... => 5
[3,1,1] generating graphics... => 4
[2,2,1] generating graphics... => 3
[2,1,1,1] generating graphics... => 2
[1,1,1,1,1] generating graphics... => 1
[6] generating graphics... => 2
[5,1] generating graphics... => 3
[4,2] generating graphics... => 5
[4,1,1] generating graphics... => 4
[3,3] generating graphics... => 4
[3,2,1] generating graphics... => 6
[3,1,1,1] generating graphics... => 3
[2,2,2] generating graphics... => 3
[2,2,1,1] generating graphics... => 2
[2,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1] generating graphics... => 1
[7] generating graphics... => 2
[6,1] generating graphics... => 3
[5,2] generating graphics... => 4
[5,1,1] generating graphics... => 3
[4,3] generating graphics... => 5
[4,2,1] generating graphics... => 7
[4,1,1,1] generating graphics... => 4
[3,3,1] generating graphics... => 6
[3,2,2] generating graphics... => 5
[3,2,1,1] generating graphics... => 4
[3,1,1,1,1] generating graphics... => 3
[2,2,2,1] generating graphics... => 3
[2,2,1,1,1] generating graphics... => 2
[2,1,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1,1] generating graphics... => 1
[8] generating graphics... => 2
[7,1] generating graphics... => 3
[6,2] generating graphics... => 4
[6,1,1] generating graphics... => 3
[5,3] generating graphics... => 5
[5,2,1] generating graphics... => 5
[5,1,1,1] generating graphics... => 4
[4,4] generating graphics... => 4
[4,3,1] generating graphics... => 8
[4,2,2] generating graphics... => 7
[4,2,1,1] generating graphics... => 6
[4,1,1,1,1] generating graphics... => 3
[3,3,2] generating graphics... => 6
[3,3,1,1] generating graphics... => 5
[3,2,2,1] generating graphics... => 4
[3,2,1,1,1] generating graphics... => 4
[3,1,1,1,1,1] generating graphics... => 3
[2,2,2,2] generating graphics... => 3
[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... => 2
[1,1,1,1,1,1,1,1] generating graphics... => 1
[9] generating graphics... => 2
[8,1] generating graphics... => 3
[7,2] generating graphics... => 4
[7,1,1] generating graphics... => 3
[6,3] generating graphics... => 4
[6,2,1] generating graphics... => 5
[6,1,1,1] generating graphics... => 3
[5,4] generating graphics... => 5
[5,3,1] generating graphics... => 7
[5,2,2] generating graphics... => 6
[5,2,1,1] generating graphics... => 5
[5,1,1,1,1] generating graphics... => 4
[4,4,1] generating graphics... => 6
[4,3,2] generating graphics... => 9
[4,3,1,1] generating graphics... => 8
[4,2,2,1] generating graphics... => 7
[4,2,1,1,1] generating graphics... => 5
[4,1,1,1,1,1] generating graphics... => 3
[3,3,3] generating graphics... => 5
[3,3,2,1] generating graphics... => 6
[3,3,1,1,1] generating graphics... => 4
[3,2,2,2] generating graphics... => 4
[3,2,2,1,1] generating graphics... => 3
[3,2,1,1,1,1] generating graphics... => 4
[3,1,1,1,1,1,1] generating graphics... => 3
[2,2,2,2,1] generating graphics... => 3
[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... => 2
[1,1,1,1,1,1,1,1,1] generating graphics... => 1
[10] generating graphics... => 2
[9,1] generating graphics... => 3
[8,2] generating graphics... => 4
[8,1,1] generating graphics... => 3
[7,3] generating graphics... => 4
[7,2,1] generating graphics... => 5
[7,1,1,1] generating graphics... => 3
[6,4] generating graphics... => 5
[6,3,1] generating graphics... => 6
[6,2,2] generating graphics... => 5
[6,2,1,1] generating graphics... => 4
[6,1,1,1,1] generating graphics... => 4
[5,5] generating graphics... => 4
[5,4,1] generating graphics... => 6
[5,3,2] generating graphics... => 9
[5,3,1,1] generating graphics... => 8
[5,2,2,1] generating graphics... => 7
[5,2,1,1,1] generating graphics... => 5
[5,1,1,1,1,1] generating graphics... => 3
[4,4,2] generating graphics... => 8
[4,4,1,1] generating graphics... => 7
[4,3,3] generating graphics... => 7
[4,3,2,1] generating graphics... => 10
[4,3,1,1,1] generating graphics... => 6
[4,2,2,2] generating graphics... => 6
[4,2,2,1,1] generating graphics... => 5
[4,2,1,1,1,1] generating graphics... => 5
[4,1,1,1,1,1,1] generating graphics... => 3
[3,3,3,1] generating graphics... => 6
[3,3,2,2] generating graphics... => 5
[3,3,2,1,1] generating graphics... => 4
[3,3,1,1,1,1] generating graphics... => 4
[3,2,2,2,1] generating graphics... => 4
[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... => 3
[2,2,2,2,2] generating graphics... => 3
[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... => 2
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[11] generating graphics... => 2
[10,1] generating graphics... => 3
[9,2] generating graphics... => 4
[9,1,1] generating graphics... => 3
[8,3] generating graphics... => 4
[8,2,1] generating graphics... => 5
[8,1,1,1] generating graphics... => 3
[7,4] generating graphics... => 4
[7,3,1] generating graphics... => 6
[7,2,2] generating graphics... => 5
[7,2,1,1] generating graphics... => 4
[7,1,1,1,1] generating graphics... => 3
[6,5] generating graphics... => 5
[6,4,1] generating graphics... => 6
[6,3,2] generating graphics... => 7
[6,3,1,1] generating graphics... => 6
[6,2,2,1] generating graphics... => 5
[6,2,1,1,1] generating graphics... => 5
[6,1,1,1,1,1] generating graphics... => 4
[5,5,1] generating graphics... => 5
[5,4,2] generating graphics... => 9
[5,4,1,1] generating graphics... => 8
[5,3,3] generating graphics... => 8
[5,3,2,1] generating graphics... => 11
[5,3,1,1,1] generating graphics... => 7
[5,2,2,2] generating graphics... => 7
[5,2,2,1,1] generating graphics... => 6
[5,2,1,1,1,1] generating graphics... => 4
[5,1,1,1,1,1,1] generating graphics... => 3
[4,4,3] generating graphics... => 7
[4,4,2,1] generating graphics... => 10
[4,4,1,1,1] generating graphics... => 6
[4,3,3,1] generating graphics... => 9
[4,3,2,2] generating graphics... => 8
[4,3,2,1,1] generating graphics... => 7
[4,3,1,1,1,1] generating graphics... => 6
[4,2,2,2,1] generating graphics... => 5
[4,2,2,1,1,1] generating graphics... => 5
[4,2,1,1,1,1,1] generating graphics... => 5
[4,1,1,1,1,1,1,1] generating graphics... => 3
[3,3,3,2] generating graphics... => 6
[3,3,3,1,1] generating graphics... => 5
[3,3,2,2,1] generating graphics... => 4
[3,3,2,1,1,1] generating graphics... => 4
[3,3,1,1,1,1,1] generating graphics... => 4
[3,2,2,2,2] generating graphics... => 4
[3,2,2,2,1,1] generating graphics... => 3
[3,2,2,1,1,1,1] generating graphics... => 3
[3,2,1,1,1,1,1,1] generating graphics... => 4
[3,1,1,1,1,1,1,1,1] generating graphics... => 3
[2,2,2,2,2,1] generating graphics... => 3
[2,2,2,2,1,1,1] generating graphics... => 2
[2,2,2,1,1,1,1,1] generating graphics... => 2
[2,2,1,1,1,1,1,1,1] generating graphics... => 2
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
[12] generating graphics... => 2
[11,1] generating graphics... => 3
[10,2] generating graphics... => 4
[10,1,1] generating graphics... => 3
[9,3] generating graphics... => 4
[9,2,1] generating graphics... => 5
[9,1,1,1] generating graphics... => 3
[8,4] generating graphics... => 4
[8,3,1] generating graphics... => 6
[8,2,2] generating graphics... => 5
[8,2,1,1] generating graphics... => 4
[8,1,1,1,1] generating graphics... => 3
[7,5] generating graphics... => 5
[7,4,1] generating graphics... => 5
[7,3,2] generating graphics... => 7
[7,3,1,1] generating graphics... => 6
[7,2,2,1] generating graphics... => 5
[7,2,1,1,1] generating graphics... => 4
[7,1,1,1,1,1] generating graphics... => 4
[6,6] generating graphics... => 4
[6,5,1] generating graphics... => 6
[6,4,2] generating graphics... => 8
[6,4,1,1] generating graphics... => 7
[6,3,3] generating graphics... => 7
[6,3,2,1] generating graphics... => 8
[6,3,1,1,1] generating graphics... => 6
[6,2,2,2] generating graphics... => 6
[6,2,2,1,1] generating graphics... => 5
[6,2,1,1,1,1] generating graphics... => 5
[6,1,1,1,1,1,1] generating graphics... => 3
[5,5,2] generating graphics... => 7
[5,5,1,1] generating graphics... => 6
[5,4,3] generating graphics... => 9
[5,4,2,1] generating graphics... => 12
[5,4,1,1,1] generating graphics... => 8
[5,3,3,1] generating graphics... => 11
[5,3,2,2] generating graphics... => 10
[5,3,2,1,1] generating graphics... => 9
[5,3,1,1,1,1] generating graphics... => 6
[5,2,2,2,1] generating graphics... => 7
[5,2,2,1,1,1] generating graphics... => 5
[5,2,1,1,1,1,1] generating graphics... => 4
[5,1,1,1,1,1,1,1] generating graphics... => 3
[4,4,4] generating graphics... => 6
[4,4,3,1] generating graphics... => 10
[4,4,2,2] generating graphics... => 9
[4,4,2,1,1] generating graphics... => 8
[4,4,1,1,1,1] generating graphics... => 5
[4,3,3,2] generating graphics... => 8
[4,3,3,1,1] generating graphics... => 7
[4,3,2,2,1] generating graphics... => 6
[4,3,2,1,1,1] generating graphics... => 7
[4,3,1,1,1,1,1] generating graphics... => 6
[4,2,2,2,2] generating graphics... => 5
[4,2,2,2,1,1] generating graphics... => 4
[4,2,2,1,1,1,1] generating graphics... => 5
[4,2,1,1,1,1,1,1] generating graphics... => 5
[4,1,1,1,1,1,1,1,1] generating graphics... => 3
[3,3,3,3] generating graphics... => 5
[3,3,3,2,1] generating graphics... => 6
[3,3,3,1,1,1] generating graphics... => 4
[3,3,2,2,2] generating graphics... => 4
[3,3,2,2,1,1] generating graphics... => 3
[3,3,2,1,1,1,1] generating graphics... => 4
[3,3,1,1,1,1,1,1] generating graphics... => 4
[3,2,2,2,2,1] generating graphics... => 4
[3,2,2,2,1,1,1] generating graphics... => 3
[3,2,2,1,1,1,1,1] generating graphics... => 3
[3,2,1,1,1,1,1,1,1] generating graphics... => 4
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 3
[2,2,2,2,2,2] generating graphics... => 3
[2,2,2,2,2,1,1] generating graphics... => 2
[2,2,2,2,1,1,1,1] generating graphics... => 2
[2,2,2,1,1,1,1,1,1] generating graphics... => 2
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 2
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 2
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1
click to show generating function       
Description
The diagonal inversion number of an integer partition.
This is the number of cells $c$ in the diagram of an integer partition $\lambda$ for which $\operatorname{arm}(c)-\operatorname{leg}(c) \in \{0,1\}$.
References
[1] Lee, K., Li, L., Loehr, N. A. A Combinatorial Approach to the Symmetry of $q,t$-Catalan Numbers arXiv:1602.01126
Code
def statistic(P):
    return sum( 1 for c in P.cells() if P.arm_length(*c)-P.leg_length(*c) in [0,1] )

Created
Feb 06, 2016 at 17:13 by Christian Stump
Updated
Oct 31, 2017 at 08:15 by Martin Rubey