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Identifier
Values
=>
Cc0002;cc-rep
[]=>0 [1]=>1 [2]=>1 [1,1]=>1 [3]=>1 [2,1]=>2 [1,1,1]=>1 [4]=>1 [3,1]=>2 [2,2]=>2 [2,1,1]=>2 [1,1,1,1]=>1 [5]=>1 [4,1]=>2 [3,2]=>2 [3,1,1]=>3 [2,2,1]=>2 [2,1,1,1]=>2 [1,1,1,1,1]=>1 [6]=>1 [5,1]=>2 [4,2]=>2 [4,1,1]=>3 [3,3]=>2 [3,2,1]=>3 [3,1,1,1]=>3 [2,2,2]=>2 [2,2,1,1]=>2 [2,1,1,1,1]=>2 [1,1,1,1,1,1]=>1 [7]=>1 [6,1]=>2 [5,2]=>2 [5,1,1]=>3 [4,3]=>2 [4,2,1]=>3 [4,1,1,1]=>4 [3,3,1]=>3 [3,2,2]=>3 [3,2,1,1]=>3 [3,1,1,1,1]=>3 [2,2,2,1]=>2 [2,2,1,1,1]=>2 [2,1,1,1,1,1]=>2 [1,1,1,1,1,1,1]=>1 [8]=>1 [7,1]=>2 [6,2]=>2 [6,1,1]=>3 [5,3]=>2 [5,2,1]=>3 [5,1,1,1]=>4 [4,4]=>2 [4,3,1]=>3 [4,2,2]=>3 [4,2,1,1]=>4 [4,1,1,1,1]=>4 [3,3,2]=>3 [3,3,1,1]=>3 [3,2,2,1]=>3 [3,2,1,1,1]=>3 [3,1,1,1,1,1]=>3 [2,2,2,2]=>2 [2,2,2,1,1]=>2 [2,2,1,1,1,1]=>2 [2,1,1,1,1,1,1]=>2 [1,1,1,1,1,1,1,1]=>1 [9]=>1 [8,1]=>2 [7,2]=>2 [7,1,1]=>3 [6,3]=>2 [6,2,1]=>3 [6,1,1,1]=>4 [5,4]=>2 [5,3,1]=>3 [5,2,2]=>3 [5,2,1,1]=>4 [5,1,1,1,1]=>5 [4,4,1]=>3 [4,3,2]=>3 [4,3,1,1]=>4 [4,2,2,1]=>4 [4,2,1,1,1]=>4 [4,1,1,1,1,1]=>4 [3,3,3]=>3 [3,3,2,1]=>3 [3,3,1,1,1]=>3 [3,2,2,2]=>3 [3,2,2,1,1]=>3 [3,2,1,1,1,1]=>3 [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]=>2 [2,1,1,1,1,1,1,1]=>2 [1,1,1,1,1,1,1,1,1]=>1 [10]=>1 [9,1]=>2 [8,2]=>2 [8,1,1]=>3 [7,3]=>2 [7,2,1]=>3 [7,1,1,1]=>4 [6,4]=>2 [6,3,1]=>3 [6,2,2]=>3 [6,2,1,1]=>4 [6,1,1,1,1]=>5 [5,5]=>2 [5,4,1]=>3 [5,3,2]=>3 [5,3,1,1]=>4 [5,2,2,1]=>4 [5,2,1,1,1]=>5 [5,1,1,1,1,1]=>5 [4,4,2]=>3 [4,4,1,1]=>4 [4,3,3]=>3 [4,3,2,1]=>4 [4,3,1,1,1]=>4 [4,2,2,2]=>4 [4,2,2,1,1]=>4 [4,2,1,1,1,1]=>4 [4,1,1,1,1,1,1]=>4 [3,3,3,1]=>3 [3,3,2,2]=>3 [3,3,2,1,1]=>3 [3,3,1,1,1,1]=>3 [3,2,2,2,1]=>3 [3,2,2,1,1,1]=>3 [3,2,1,1,1,1,1]=>3 [3,1,1,1,1,1,1,1]=>3 [2,2,2,2,2]=>2 [2,2,2,2,1,1]=>2 [2,2,2,1,1,1,1]=>2 [2,2,1,1,1,1,1,1]=>2 [2,1,1,1,1,1,1,1,1]=>2 [1,1,1,1,1,1,1,1,1,1]=>1 [11]=>1 [10,1]=>2 [9,2]=>2 [9,1,1]=>3 [8,3]=>2 [8,2,1]=>3 [8,1,1,1]=>4 [7,4]=>2 [7,3,1]=>3 [7,2,2]=>3 [7,2,1,1]=>4 [7,1,1,1,1]=>5 [6,5]=>2 [6,4,1]=>3 [6,3,2]=>3 [6,3,1,1]=>4 [6,2,2,1]=>4 [6,2,1,1,1]=>5 [6,1,1,1,1,1]=>6 [5,5,1]=>3 [5,4,2]=>3 [5,4,1,1]=>4 [5,3,3]=>3 [5,3,2,1]=>4 [5,3,1,1,1]=>5 [5,2,2,2]=>4 [5,2,2,1,1]=>5 [5,2,1,1,1,1]=>5 [5,1,1,1,1,1,1]=>5 [4,4,3]=>3 [4,4,2,1]=>4 [4,4,1,1,1]=>4 [4,3,3,1]=>4 [4,3,2,2]=>4 [4,3,2,1,1]=>4 [4,3,1,1,1,1]=>4 [4,2,2,2,1]=>4 [4,2,2,1,1,1]=>4 [4,2,1,1,1,1,1]=>4 [4,1,1,1,1,1,1,1]=>4 [3,3,3,2]=>3 [3,3,3,1,1]=>3 [3,3,2,2,1]=>3 [3,3,2,1,1,1]=>3 [3,3,1,1,1,1,1]=>3 [3,2,2,2,2]=>3 [3,2,2,2,1,1]=>3 [3,2,2,1,1,1,1]=>3 [3,2,1,1,1,1,1,1]=>3 [3,1,1,1,1,1,1,1,1]=>3 [2,2,2,2,2,1]=>2 [2,2,2,2,1,1,1]=>2 [2,2,2,1,1,1,1,1]=>2 [2,2,1,1,1,1,1,1,1]=>2 [2,1,1,1,1,1,1,1,1,1]=>2 [1,1,1,1,1,1,1,1,1,1,1]=>1 [12]=>1 [11,1]=>2 [10,2]=>2 [10,1,1]=>3 [9,3]=>2 [9,2,1]=>3 [9,1,1,1]=>4 [8,4]=>2 [8,3,1]=>3 [8,2,2]=>3 [8,2,1,1]=>4 [8,1,1,1,1]=>5 [7,5]=>2 [7,4,1]=>3 [7,3,2]=>3 [7,3,1,1]=>4 [7,2,2,1]=>4 [7,2,1,1,1]=>5 [7,1,1,1,1,1]=>6 [6,6]=>2 [6,5,1]=>3 [6,4,2]=>3 [6,4,1,1]=>4 [6,3,3]=>3 [6,3,2,1]=>4 [6,3,1,1,1]=>5 [6,2,2,2]=>4 [6,2,2,1,1]=>5 [6,2,1,1,1,1]=>6 [6,1,1,1,1,1,1]=>6 [5,5,2]=>3 [5,5,1,1]=>4 [5,4,3]=>3 [5,4,2,1]=>4 [5,4,1,1,1]=>5 [5,3,3,1]=>4 [5,3,2,2]=>4 [5,3,2,1,1]=>5 [5,3,1,1,1,1]=>5 [5,2,2,2,1]=>5 [5,2,2,1,1,1]=>5 [5,2,1,1,1,1,1]=>5 [5,1,1,1,1,1,1,1]=>5 [4,4,4]=>3 [4,4,3,1]=>4 [4,4,2,2]=>4 [4,4,2,1,1]=>4 [4,4,1,1,1,1]=>4 [4,3,3,2]=>4 [4,3,3,1,1]=>4 [4,3,2,2,1]=>4 [4,3,2,1,1,1]=>4 [4,3,1,1,1,1,1]=>4 [4,2,2,2,2]=>4 [4,2,2,2,1,1]=>4 [4,2,2,1,1,1,1]=>4 [4,2,1,1,1,1,1,1]=>4 [4,1,1,1,1,1,1,1,1]=>4 [3,3,3,3]=>3 [3,3,3,2,1]=>3 [3,3,3,1,1,1]=>3 [3,3,2,2,2]=>3 [3,3,2,2,1,1]=>3 [3,3,2,1,1,1,1]=>3 [3,3,1,1,1,1,1,1]=>3 [3,2,2,2,2,1]=>3 [3,2,2,2,1,1,1]=>3 [3,2,2,1,1,1,1,1]=>3 [3,2,1,1,1,1,1,1,1]=>3 [3,1,1,1,1,1,1,1,1,1]=>3 [2,2,2,2,2,2]=>2 [2,2,2,2,2,1,1]=>2 [2,2,2,2,1,1,1,1]=>2 [2,2,2,1,1,1,1,1,1]=>2 [2,2,1,1,1,1,1,1,1,1]=>2 [2,1,1,1,1,1,1,1,1,1,1]=>2 [1,1,1,1,1,1,1,1,1,1,1,1]=>1 [5,5,3]=>3 [5,4,4]=>3 [5,4,3,1]=>4 [5,4,2,2]=>4 [5,4,2,1,1]=>5 [5,3,3,2]=>4 [5,3,3,1,1]=>5 [5,3,2,2,1]=>5 [4,4,4,1]=>4 [4,4,3,2]=>4 [4,4,3,1,1]=>4 [4,4,2,2,1]=>4 [4,3,3,3]=>4 [4,3,3,2,1]=>4 [3,3,3,3,1]=>3 [3,3,3,2,2]=>3 [5,5,4]=>3 [5,4,3,2]=>4 [5,4,3,1,1]=>5 [5,4,2,2,1]=>5 [5,3,3,2,1]=>5 [4,4,4,2]=>4 [4,4,3,3]=>4 [4,4,3,2,1]=>4 [3,3,3,3,2]=>3 [5,5,5]=>3 [5,4,3,2,1]=>5 [4,4,4,3]=>4 [3,3,3,3,3]=>3 [7,5,3,1]=>4 [4,4,4,4]=>4 [7,5,4,3,1]=>5 [6,5,4,3,2,1]=>6 [11,7,5,1]=>4 [9,7,5,3,1]=>5 [7,6,5,4,3,2,1]=>7 [9,7,5,5,3,1]=>6 [11,9,7,5,3,1]=>6 [11,8,7,5,4,1]=>6 [8,7,6,5,4,3,2,1]=>8 [11,9,7,6,5,3,1]=>7 [13,11,9,7,5,3,1]=>7 [13,11,9,7,7,5,3,1]=>8 [17,13,11,9,7,5,1]=>7 [15,13,11,9,7,5,3,1]=>8 [29,23,19,17,13,11,7,1]=>8
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Description
The minimum of the number of parts and the size of the first part of an integer partition.
This is also an upper bound on the maximal number of non-attacking rooks that can be placed on the Ferrers board.
References
[1] wikipedia:Rook_polynomial
Code
def statistic(la):
    if la:
        return min(la[0], len(la))
    return 0
Created
Jun 10, 2016 at 23:43 by Martin Rubey
Updated
Dec 22, 2020 at 13:16 by Martin Rubey