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Identifier
Values
=>
Cc0002;cc-rep
[]=>0 [1]=>0 [2]=>1 [1,1]=>0 [3]=>1 [2,1]=>0 [1,1,1]=>0 [4]=>2 [3,1]=>1 [2,2]=>1 [2,1,1]=>0 [1,1,1,1]=>0 [5]=>2 [4,1]=>1 [3,2]=>1 [3,1,1]=>1 [2,2,1]=>0 [2,1,1,1]=>0 [1,1,1,1,1]=>0 [6]=>3 [5,1]=>2 [4,2]=>2 [4,1,1]=>1 [3,3]=>1 [3,2,1]=>0 [3,1,1,1]=>1 [2,2,2]=>1 [2,2,1,1]=>0 [2,1,1,1,1]=>0 [1,1,1,1,1,1]=>0 [7]=>3 [6,1]=>2 [5,2]=>2 [5,1,1]=>2 [4,3]=>1 [4,2,1]=>1 [4,1,1,1]=>1 [3,3,1]=>1 [3,2,2]=>1 [3,2,1,1]=>0 [3,1,1,1,1]=>1 [2,2,2,1]=>0 [2,2,1,1,1]=>0 [2,1,1,1,1,1]=>0 [1,1,1,1,1,1,1]=>0 [8]=>4 [7,1]=>3 [6,2]=>3 [6,1,1]=>2 [5,3]=>2 [5,2,1]=>1 [5,1,1,1]=>2 [4,4]=>2 [4,3,1]=>1 [4,2,2]=>2 [4,2,1,1]=>1 [4,1,1,1,1]=>1 [3,3,2]=>1 [3,3,1,1]=>1 [3,2,2,1]=>0 [3,2,1,1,1]=>0 [3,1,1,1,1,1]=>1 [2,2,2,2]=>1 [2,2,2,1,1]=>0 [2,2,1,1,1,1]=>0 [2,1,1,1,1,1,1]=>0 [1,1,1,1,1,1,1,1]=>0 [9]=>4 [8,1]=>3 [7,2]=>3 [7,1,1]=>3 [6,3]=>2 [6,2,1]=>2 [6,1,1,1]=>2 [5,4]=>2 [5,3,1]=>2 [5,2,2]=>2 [5,2,1,1]=>1 [5,1,1,1,1]=>2 [4,4,1]=>1 [4,3,2]=>1 [4,3,1,1]=>1 [4,2,2,1]=>1 [4,2,1,1,1]=>1 [4,1,1,1,1,1]=>1 [3,3,3]=>1 [3,3,2,1]=>0 [3,3,1,1,1]=>1 [3,2,2,2]=>1 [3,2,2,1,1]=>0 [3,2,1,1,1,1]=>0 [3,1,1,1,1,1,1]=>1 [2,2,2,2,1]=>0 [2,2,2,1,1,1]=>0 [2,2,1,1,1,1,1]=>0 [2,1,1,1,1,1,1,1]=>0 [1,1,1,1,1,1,1,1,1]=>0 [10]=>5 [9,1]=>4 [8,2]=>4 [8,1,1]=>3 [7,3]=>3 [7,2,1]=>2 [7,1,1,1]=>3 [6,4]=>3 [6,3,1]=>2 [6,2,2]=>3 [6,2,1,1]=>2 [6,1,1,1,1]=>2 [5,5]=>2 [5,4,1]=>1 [5,3,2]=>2 [5,3,1,1]=>2 [5,2,2,1]=>1 [5,2,1,1,1]=>1 [5,1,1,1,1,1]=>2 [4,4,2]=>2 [4,4,1,1]=>1 [4,3,3]=>1 [4,3,2,1]=>0 [4,3,1,1,1]=>1 [4,2,2,2]=>2 [4,2,2,1,1]=>1 [4,2,1,1,1,1]=>1 [4,1,1,1,1,1,1]=>1 [3,3,3,1]=>1 [3,3,2,2]=>1 [3,3,2,1,1]=>0 [3,3,1,1,1,1]=>1 [3,2,2,2,1]=>0 [3,2,2,1,1,1]=>0 [3,2,1,1,1,1,1]=>0 [3,1,1,1,1,1,1,1]=>1 [2,2,2,2,2]=>1 [2,2,2,2,1,1]=>0 [2,2,2,1,1,1,1]=>0 [2,2,1,1,1,1,1,1]=>0 [2,1,1,1,1,1,1,1,1]=>0 [1,1,1,1,1,1,1,1,1,1]=>0
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Description
The number of cells of the partition whose leg is zero and arm is odd.
This statistic is equidistributed with St000143The largest repeated part of a partition., see [1].
References
[1] Tim Statistics on partitions equidistributed with number of even parts MathOverflow:134577
Code
def good_cells(L):
    return [ c for c in L.cells() if L.leg_length(*c) == 0 and L.arm_length(*c) % 2 == 1 ]

def statistic(x):
    return len(good_cells(x))
Created
Jul 08, 2013 at 13:27 by Christian Stump
Updated
Oct 29, 2017 at 16:06 by Martin Rubey