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Identifier
Values
=>
Cc0002;cc-rep
[]=>0 [1]=>0 [2]=>0 [1,1]=>1 [3]=>0 [2,1]=>0 [1,1,1]=>1 [4]=>0 [3,1]=>0 [2,2]=>1 [2,1,1]=>1 [1,1,1,1]=>2 [5]=>0 [4,1]=>0 [3,2]=>0 [3,1,1]=>1 [2,2,1]=>1 [2,1,1,1]=>1 [1,1,1,1,1]=>2 [6]=>0 [5,1]=>0 [4,2]=>0 [4,1,1]=>1 [3,3]=>1 [3,2,1]=>0 [3,1,1,1]=>1 [2,2,2]=>1 [2,2,1,1]=>2 [2,1,1,1,1]=>2 [1,1,1,1,1,1]=>3 [7]=>0 [6,1]=>0 [5,2]=>0 [5,1,1]=>1 [4,3]=>0 [4,2,1]=>0 [4,1,1,1]=>1 [3,3,1]=>1 [3,2,2]=>1 [3,2,1,1]=>1 [3,1,1,1,1]=>2 [2,2,2,1]=>1 [2,2,1,1,1]=>2 [2,1,1,1,1,1]=>2 [1,1,1,1,1,1,1]=>3 [8]=>0 [7,1]=>0 [6,2]=>0 [6,1,1]=>1 [5,3]=>0 [5,2,1]=>0 [5,1,1,1]=>1 [4,4]=>1 [4,3,1]=>0 [4,2,2]=>1 [4,2,1,1]=>1 [4,1,1,1,1]=>2 [3,3,2]=>1 [3,3,1,1]=>2 [3,2,2,1]=>1 [3,2,1,1,1]=>1 [3,1,1,1,1,1]=>2 [2,2,2,2]=>2 [2,2,2,1,1]=>2 [2,2,1,1,1,1]=>3 [2,1,1,1,1,1,1]=>3 [1,1,1,1,1,1,1,1]=>4 [9]=>0 [8,1]=>0 [7,2]=>0 [7,1,1]=>1 [6,3]=>0 [6,2,1]=>0 [6,1,1,1]=>1 [5,4]=>0 [5,3,1]=>0 [5,2,2]=>1 [5,2,1,1]=>1 [5,1,1,1,1]=>2 [4,4,1]=>1 [4,3,2]=>0 [4,3,1,1]=>1 [4,2,2,1]=>1 [4,2,1,1,1]=>1 [4,1,1,1,1,1]=>2 [3,3,3]=>1 [3,3,2,1]=>1 [3,3,1,1,1]=>2 [3,2,2,2]=>1 [3,2,2,1,1]=>2 [3,2,1,1,1,1]=>2 [3,1,1,1,1,1,1]=>3 [2,2,2,2,1]=>2 [2,2,2,1,1,1]=>2 [2,2,1,1,1,1,1]=>3 [2,1,1,1,1,1,1,1]=>3 [1,1,1,1,1,1,1,1,1]=>4 [10]=>0 [9,1]=>0 [8,2]=>0 [8,1,1]=>1 [7,3]=>0 [7,2,1]=>0 [7,1,1,1]=>1 [6,4]=>0 [6,3,1]=>0 [6,2,2]=>1 [6,2,1,1]=>1 [6,1,1,1,1]=>2 [5,5]=>1 [5,4,1]=>0 [5,3,2]=>0 [5,3,1,1]=>1 [5,2,2,1]=>1 [5,2,1,1,1]=>1 [5,1,1,1,1,1]=>2 [4,4,2]=>1 [4,4,1,1]=>2 [4,3,3]=>1 [4,3,2,1]=>0 [4,3,1,1,1]=>1 [4,2,2,2]=>1 [4,2,2,1,1]=>2 [4,2,1,1,1,1]=>2 [4,1,1,1,1,1,1]=>3 [3,3,3,1]=>1 [3,3,2,2]=>2 [3,3,2,1,1]=>2 [3,3,1,1,1,1]=>3 [3,2,2,2,1]=>1 [3,2,2,1,1,1]=>2 [3,2,1,1,1,1,1]=>2 [3,1,1,1,1,1,1,1]=>3 [2,2,2,2,2]=>2 [2,2,2,2,1,1]=>3 [2,2,2,1,1,1,1]=>3 [2,2,1,1,1,1,1,1]=>4 [2,1,1,1,1,1,1,1,1]=>4 [1,1,1,1,1,1,1,1,1,1]=>5 [5,4,2]=>0 [5,4,1,1]=>1 [5,3,3]=>1 [5,3,2,1]=>0 [5,3,1,1,1]=>1 [5,2,2,2]=>1 [5,2,2,1,1]=>2 [4,4,3]=>1 [4,4,2,1]=>1 [4,4,1,1,1]=>2 [4,3,3,1]=>1 [4,3,2,2]=>1 [4,3,2,1,1]=>1 [4,2,2,2,1]=>1 [3,3,3,2]=>1 [3,3,3,1,1]=>2 [3,3,2,2,1]=>2 [6,4,2]=>0 [5,4,3]=>0 [5,4,2,1]=>0 [5,4,1,1,1]=>1 [5,3,3,1]=>1 [5,3,2,2]=>1 [5,3,2,1,1]=>1 [5,2,2,2,1]=>1 [4,4,3,1]=>1 [4,4,2,2]=>2 [4,4,2,1,1]=>2 [4,3,3,2]=>1 [4,3,3,1,1]=>2 [4,3,2,2,1]=>1 [3,3,3,2,1]=>1 [3,3,2,2,1,1]=>3 [5,4,3,1]=>0 [5,4,2,2]=>1 [5,4,2,1,1]=>1 [5,3,3,2]=>1 [5,3,3,1,1]=>2 [5,3,2,2,1]=>1 [4,4,3,2]=>1 [4,4,3,1,1]=>2 [4,4,2,2,1]=>2 [4,3,3,2,1]=>1 [5,4,3,2]=>0 [5,4,3,1,1]=>1 [5,4,2,2,1]=>1 [5,3,3,2,1]=>1 [4,4,3,2,1]=>1 [5,4,3,2,1]=>0 [7,5,3,1]=>0 [7,5,4,3,1]=>0 [6,5,4,3,2,1]=>0 [11,7,5,1]=>0 [9,7,5,3,1]=>0 [7,6,5,4,3,2,1]=>0 [9,7,5,5,3,1]=>1 [11,9,7,5,3,1]=>0 [11,8,7,5,4,1]=>0 [8,7,6,5,4,3,2,1]=>0 [11,9,7,6,5,3,1]=>0 [13,11,9,7,5,3,1]=>0 [13,11,9,7,7,5,3,1]=>1 [17,13,11,9,7,5,1]=>0 [15,13,11,9,7,5,3,1]=>0 [29,23,19,17,13,11,7,1]=>0
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Description
The floored half-sum of the multiplicities of a partition.
This statistic is equidistributed with St000143The largest repeated part of a partition. and St000149The number of cells of the partition whose leg is zero and arm is odd., see [1].
References
[1] Tim Statistics on partitions equidistributed with number of even parts MathOverflow:134577
Code
def statistic(L):
    E = L.to_exp()
    return sum( floor( e/2 ) for e in E )
Created
Jul 08, 2013 at 13:35 by Christian Stump
Updated
Sep 09, 2020 at 21:28 by Martin Rubey