- FindStat

Identifier

St000944: Integer partitions ⟶ ℤ

Values

=>
                            Cc0002;cc-rep
                            
                            
                            

                        [1]=>0
[2]=>0
[1,1]=>0
[3]=>1
[2,1]=>1
[1,1,1]=>0
[4]=>1
[3,1]=>0
[2,2]=>1
[2,1,1]=>0
[1,1,1,1]=>0
[5]=>1
[4,1]=>4
[3,2]=>1
[3,1,1]=>0
[2,2,1]=>4
[2,1,1,1]=>0
[1,1,1,1,1]=>0
[6]=>2
[5,1]=>9
[4,2]=>0
[4,1,1]=>16
[3,3]=>6
[3,2,1]=>16
[3,1,1,1]=>4
[2,2,2]=>4
[2,2,1,1]=>0
[2,1,1,1,1]=>1
[1,1,1,1,1,1]=>0
[7]=>2
[6,1]=>6
[5,2]=>27
[5,1,1]=>15
[4,3]=>15
[4,2,1]=>42
[4,1,1,1]=>20
[3,3,1]=>6
[3,2,2]=>15
[3,2,1,1]=>28
[3,1,1,1,1]=>0
[2,2,2,1]=>13
[2,2,1,1,1]=>1
[2,1,1,1,1,1]=>0
[1,1,1,1,1,1,1]=>0
[8]=>2
[7,1]=>14
[6,2]=>33
[6,1,1]=>21
[5,3]=>56
[5,2,1]=>99
[5,1,1,1]=>35
[4,4]=>15
[4,3,1]=>49
[4,2,2]=>78
[4,2,1,1]=>0
[4,1,1,1,1]=>35
[3,3,2]=>21
[3,3,1,1]=>34
[3,2,2,1]=>91
[3,2,1,1,1]=>29
[3,1,1,1,1,1]=>0
[2,2,2,2]=>13
[2,2,2,1,1]=>0
[2,2,1,1,1,1]=>7
[2,1,1,1,1,1,1]=>0
[1,1,1,1,1,1,1,1]=>0
[9]=>3
[8,1]=>23
[7,2]=>27
[7,1,1]=>77
[6,3]=>137
[6,2,1]=>238
[6,1,1,1]=>91
[5,4]=>85
[5,3,1]=>0
[5,2,2]=>233
[5,2,1,1]=>189
[5,1,1,1,1]=>105
[4,4,1]=>134
[4,3,2]=>232
[4,3,1,1]=>27
[4,2,2,1]=>189
[4,2,1,1,1]=>0
[4,1,1,1,1,1]=>77
[3,3,3]=>63
[3,3,2,1]=>272
[3,3,1,1,1]=>127
[3,2,2,2]=>118
[3,2,2,1,1]=>0
[3,2,1,1,1,1]=>77
[3,1,1,1,1,1,1]=>7
[2,2,2,2,1]=>41
[2,2,2,1,1,1]=>7
[2,2,1,1,1,1,1]=>0
[2,1,1,1,1,1,1,1]=>1
[1,1,1,1,1,1,1,1,1]=>0
[10]=>4
[9,1]=>18
[8,2]=>138
[8,1,1]=>72
[7,3]=>191
[7,2,1]=>496
[7,1,1,1]=>168
[6,4]=>180
[6,3,1]=>594
[6,2,2]=>351
[6,2,1,1]=>1064
[6,1,1,1,1]=>126
[5,5]=>85
[5,4,1]=>297
[5,3,2]=>297
[5,3,1,1]=>0
[5,2,2,1]=>1232
[5,2,1,1,1]=>896
[5,1,1,1,1,1]=>126
[4,4,2]=>198
[4,4,1,1]=>593
[4,3,3]=>463
[4,3,2,1]=>1152
[4,3,1,1,1]=>343
[4,2,2,2]=>307
[4,2,2,1,1]=>0
[4,2,1,1,1,1]=>336
[4,1,1,1,1,1,1]=>84
[3,3,3,1]=>167
[3,3,2,2]=>306
[3,3,2,1,1]=>603
[3,3,1,1,1,1]=>99
[3,2,2,2,1]=>279
[3,2,2,1,1,1]=>36
[3,2,1,1,1,1,1]=>144
[3,1,1,1,1,1,1,1]=>0
[2,2,2,2,2]=>41
[2,2,2,2,1,1]=>0
[2,2,2,1,1,1,1]=>34
[2,2,1,1,1,1,1,1]=>2
[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 3-degree of an integer partition.
For an integer partition $\lambda$, this is given by the exponent of 3 in the Gram determinant of the integal Specht module of the symmetric group indexed by $\lambda$.
This stupid comment should not be accepted as an edit!

References

[1] noreference given

Code

def statistic(L):
    return L.prime_degree(3)

Created

Aug 22, 2017 at 01:24 by Martin Rubey

Updated

Aug 22, 2017 at 10:43 by Christian Stump