Identifier
- St000149: Integer partitions ⟶ ℤ
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].
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
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