Identifier
Values
=>
Cc0002;cc-rep
[]=>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
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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 $GL_3$.
This is also the dimension of the corresponding irreducible representation of $GL_3$.
Code
def statistic(mu):
return SemistandardTableaux(shape=mu, max_entry=3).cardinality()
Created
Mar 21, 2017 at 07:34 by Martin Rubey
Updated
Apr 26, 2018 at 07:24 by Martin Rubey
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