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-----------------------------------------------------------------------------
Statistic identifier: St000715
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The number of semistandard Young tableaux of given shape and entries at most 3.
This is also the dimension of the corresponding irreducible representation of $GL_3$.
-----------------------------------------------------------------------------
References: [1] [[wikipedia:Young_tableau#Applications_in_representation_theory]]
-----------------------------------------------------------------------------
Code:
def statistic(mu):
return SemistandardTableaux(shape=mu, max_entry=3).cardinality()
-----------------------------------------------------------------------------
Statistic values:
[] => 1
[1] => 3
[2] => 6
[1,1] => 3
[3] => 10
[2,1] => 8
[1,1,1] => 1
[4] => 15
[3,1] => 15
[2,2] => 6
[2,1,1] => 3
[1,1,1,1] => 0
[5] => 21
[4,1] => 24
[3,2] => 15
[3,1,1] => 6
[2,2,1] => 3
[2,1,1,1] => 0
[1,1,1,1,1] => 0
[6] => 28
[5,1] => 35
[4,2] => 27
[4,1,1] => 10
[3,3] => 10
[3,2,1] => 8
[3,1,1,1] => 0
[2,2,2] => 1
[2,2,1,1] => 0
[2,1,1,1,1] => 0
[1,1,1,1,1,1] => 0
[7] => 36
[6,1] => 48
[5,2] => 42
[5,1,1] => 15
[4,3] => 24
[4,2,1] => 15
[4,1,1,1] => 0
[3,3,1] => 6
[3,2,2] => 3
[3,2,1,1] => 0
[3,1,1,1,1] => 0
[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] => 45
[7,1] => 63
[6,2] => 60
[6,1,1] => 21
[5,3] => 42
[5,2,1] => 24
[5,1,1,1] => 0
[4,4] => 15
[4,3,1] => 15
[4,2,2] => 6
[4,2,1,1] => 0
[4,1,1,1,1] => 0
[3,3,2] => 3
[3,3,1,1] => 0
[3,2,2,1] => 0
[3,2,1,1,1] => 0
[3,1,1,1,1,1] => 0
[2,2,2,2] => 0
[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] => 55
[8,1] => 80
[7,2] => 81
[7,1,1] => 28
[6,3] => 64
[6,2,1] => 35
[6,1,1,1] => 0
[5,4] => 35
[5,3,1] => 27
[5,2,2] => 10
[5,2,1,1] => 0
[5,1,1,1,1] => 0
[4,4,1] => 10
[4,3,2] => 8
[4,3,1,1] => 0
[4,2,2,1] => 0
[4,2,1,1,1] => 0
[4,1,1,1,1,1] => 0
[3,3,3] => 1
[3,3,2,1] => 0
[3,3,1,1,1] => 0
[3,2,2,2] => 0
[3,2,2,1,1] => 0
[3,2,1,1,1,1] => 0
[3,1,1,1,1,1,1] => 0
[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] => 66
[9,1] => 99
[8,2] => 105
[8,1,1] => 36
[7,3] => 90
[7,2,1] => 48
[7,1,1,1] => 0
[6,4] => 60
[6,3,1] => 42
[6,2,2] => 15
[6,2,1,1] => 0
[6,1,1,1,1] => 0
[5,5] => 21
[5,4,1] => 24
[5,3,2] => 15
[5,3,1,1] => 0
[5,2,2,1] => 0
[5,2,1,1,1] => 0
[5,1,1,1,1,1] => 0
[4,4,2] => 6
[4,4,1,1] => 0
[4,3,3] => 3
[4,3,2,1] => 0
[4,3,1,1,1] => 0
[4,2,2,2] => 0
[4,2,2,1,1] => 0
[4,2,1,1,1,1] => 0
[4,1,1,1,1,1,1] => 0
[3,3,3,1] => 0
[3,3,2,2] => 0
[3,3,2,1,1] => 0
[3,3,1,1,1,1] => 0
[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] => 0
[2,2,2,2,2] => 0
[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
[11] => 78
[10,1] => 120
[9,2] => 132
[9,1,1] => 45
[8,3] => 120
[8,2,1] => 63
[8,1,1,1] => 0
[7,4] => 90
[7,3,1] => 60
[7,2,2] => 21
[7,2,1,1] => 0
[7,1,1,1,1] => 0
[6,5] => 48
[6,4,1] => 42
[6,3,2] => 24
[6,3,1,1] => 0
[6,2,2,1] => 0
[6,2,1,1,1] => 0
[6,1,1,1,1,1] => 0
[5,5,1] => 15
[5,4,2] => 15
[5,4,1,1] => 0
[5,3,3] => 6
[5,3,2,1] => 0
[5,3,1,1,1] => 0
[5,2,2,2] => 0
[5,2,2,1,1] => 0
[5,2,1,1,1,1] => 0
[5,1,1,1,1,1,1] => 0
[4,4,3] => 3
[4,4,2,1] => 0
[4,4,1,1,1] => 0
[4,3,3,1] => 0
[4,3,2,2] => 0
[4,3,2,1,1] => 0
[4,3,1,1,1,1] => 0
[4,2,2,2,1] => 0
[4,2,2,1,1,1] => 0
[4,2,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1] => 0
[3,3,3,2] => 0
[3,3,3,1,1] => 0
[3,3,2,2,1] => 0
[3,3,2,1,1,1] => 0
[3,3,1,1,1,1,1] => 0
[3,2,2,2,2] => 0
[3,2,2,2,1,1] => 0
[3,2,2,1,1,1,1] => 0
[3,2,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,1] => 0
[2,2,2,2,1,1,1] => 0
[2,2,2,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1] => 0
[12] => 91
[11,1] => 143
[10,2] => 162
[10,1,1] => 55
[9,3] => 154
[9,2,1] => 80
[9,1,1,1] => 0
[8,4] => 125
[8,3,1] => 81
[8,2,2] => 28
[8,2,1,1] => 0
[8,1,1,1,1] => 0
[7,5] => 81
[7,4,1] => 64
[7,3,2] => 35
[7,3,1,1] => 0
[7,2,2,1] => 0
[7,2,1,1,1] => 0
[7,1,1,1,1,1] => 0
[6,6] => 28
[6,5,1] => 35
[6,4,2] => 27
[6,4,1,1] => 0
[6,3,3] => 10
[6,3,2,1] => 0
[6,3,1,1,1] => 0
[6,2,2,2] => 0
[6,2,2,1,1] => 0
[6,2,1,1,1,1] => 0
[6,1,1,1,1,1,1] => 0
[5,5,2] => 10
[5,5,1,1] => 0
[5,4,3] => 8
[5,4,2,1] => 0
[5,4,1,1,1] => 0
[5,3,3,1] => 0
[5,3,2,2] => 0
[5,3,2,1,1] => 0
[5,3,1,1,1,1] => 0
[5,2,2,2,1] => 0
[5,2,2,1,1,1] => 0
[5,2,1,1,1,1,1] => 0
[5,1,1,1,1,1,1,1] => 0
[4,4,4] => 1
[4,4,3,1] => 0
[4,4,2,2] => 0
[4,4,2,1,1] => 0
[4,4,1,1,1,1] => 0
[4,3,3,2] => 0
[4,3,3,1,1] => 0
[4,3,2,2,1] => 0
[4,3,2,1,1,1] => 0
[4,3,1,1,1,1,1] => 0
[4,2,2,2,2] => 0
[4,2,2,2,1,1] => 0
[4,2,2,1,1,1,1] => 0
[4,2,1,1,1,1,1,1] => 0
[4,1,1,1,1,1,1,1,1] => 0
[3,3,3,3] => 0
[3,3,3,2,1] => 0
[3,3,3,1,1,1] => 0
[3,3,2,2,2] => 0
[3,3,2,2,1,1] => 0
[3,3,2,1,1,1,1] => 0
[3,3,1,1,1,1,1,1] => 0
[3,2,2,2,2,1] => 0
[3,2,2,2,1,1,1] => 0
[3,2,2,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1] => 0
[2,2,2,2,2,2] => 0
[2,2,2,2,2,1,1] => 0
[2,2,2,2,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1] => 0
[5,4,3,1] => 0
[5,4,2,2] => 0
[5,4,2,1,1] => 0
[5,3,3,2] => 0
[5,3,3,1,1] => 0
[5,3,2,2,1] => 0
[4,4,3,2] => 0
[4,4,3,1,1] => 0
[4,4,2,2,1] => 0
[4,3,3,2,1] => 0
[5,4,3,2] => 0
[5,4,3,1,1] => 0
[5,4,2,2,1] => 0
[5,3,3,2,1] => 0
[4,4,3,2,1] => 0
[5,4,3,2,1] => 0
-----------------------------------------------------------------------------
Created: Mar 21, 2017 at 07:34 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Apr 26, 2018 at 07:24 by Martin Rubey