- FindStat

Identifier

St000321: Integer partitions ⟶ ℤ

Values

=>
                            Cc0002;cc-rep
                            
                            
                            

                        []=>1
[1]=>1
[2]=>2
[1,1]=>1
[3]=>3
[2,1]=>2
[1,1,1]=>1
[4]=>5
[3,1]=>4
[2,2]=>3
[2,1,1]=>2
[1,1,1,1]=>1
[5]=>7
[4,1]=>6
[3,2]=>5
[3,1,1]=>4
[2,2,1]=>3
[2,1,1,1]=>2
[1,1,1,1,1]=>1
[6]=>11
[5,1]=>10
[4,2]=>9
[4,1,1]=>7
[3,3]=>7
[3,2,1]=>6
[3,1,1,1]=>4
[2,2,2]=>4
[2,2,1,1]=>3
[2,1,1,1,1]=>2
[1,1,1,1,1,1]=>1
[7]=>15
[6,1]=>14
[5,2]=>13
[5,1,1]=>11
[4,3]=>11
[4,2,1]=>10
[4,1,1,1]=>7
[3,3,1]=>8
[3,2,2]=>7
[3,2,1,1]=>6
[3,1,1,1,1]=>4
[2,2,2,1]=>4
[2,2,1,1,1]=>3
[2,1,1,1,1,1]=>2
[1,1,1,1,1,1,1]=>1
[8]=>22
[7,1]=>21
[6,2]=>20
[6,1,1]=>17
[5,3]=>18
[5,2,1]=>16
[5,1,1,1]=>12
[4,4]=>15
[4,3,1]=>14
[4,2,2]=>13
[4,2,1,1]=>11
[4,1,1,1,1]=>7
[3,3,2]=>10
[3,3,1,1]=>9
[3,2,2,1]=>8
[3,2,1,1,1]=>6
[3,1,1,1,1,1]=>4
[2,2,2,2]=>5
[2,2,2,1,1]=>4
[2,2,1,1,1,1]=>3
[2,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1]=>1
[9]=>30
[8,1]=>29
[7,2]=>28
[7,1,1]=>25
[6,3]=>26
[6,2,1]=>24
[6,1,1,1]=>18
[5,4]=>23
[5,3,1]=>22
[5,2,2]=>20
[5,2,1,1]=>17
[5,1,1,1,1]=>12
[4,4,1]=>18
[4,3,2]=>17
[4,3,1,1]=>15
[4,2,2,1]=>14
[4,2,1,1,1]=>11
[4,1,1,1,1,1]=>7
[3,3,3]=>12
[3,3,2,1]=>11
[3,3,1,1,1]=>9
[3,2,2,2]=>9
[3,2,2,1,1]=>8
[3,2,1,1,1,1]=>6
[3,1,1,1,1,1,1]=>4
[2,2,2,2,1]=>5
[2,2,2,1,1,1]=>4
[2,2,1,1,1,1,1]=>3
[2,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1]=>1
[10]=>42
[9,1]=>41
[8,2]=>40
[8,1,1]=>36
[7,3]=>38
[7,2,1]=>35
[7,1,1,1]=>28
[6,4]=>35
[6,3,1]=>33
[6,2,2]=>31
[6,2,1,1]=>27
[6,1,1,1,1]=>19
[5,5]=>30
[5,4,1]=>29
[5,3,2]=>28
[5,3,1,1]=>25
[5,2,2,1]=>23
[5,2,1,1,1]=>18
[5,1,1,1,1,1]=>12
[4,4,2]=>23
[4,4,1,1]=>21
[4,3,3]=>21
[4,3,2,1]=>20
[4,3,1,1,1]=>16
[4,2,2,2]=>17
[4,2,2,1,1]=>15
[4,2,1,1,1,1]=>11
[4,1,1,1,1,1,1]=>7
[3,3,3,1]=>14
[3,3,2,2]=>13
[3,3,2,1,1]=>12
[3,3,1,1,1,1]=>9
[3,2,2,2,1]=>10
[3,2,2,1,1,1]=>8
[3,2,1,1,1,1,1]=>6
[3,1,1,1,1,1,1,1]=>4
[2,2,2,2,2]=>6
[2,2,2,2,1,1]=>5
[2,2,2,1,1,1,1]=>4
[2,2,1,1,1,1,1,1]=>3
[2,1,1,1,1,1,1,1,1]=>2
[1,1,1,1,1,1,1,1,1,1]=>1
                    

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Description

The number of integer partitions of n that are dominated by an integer partition.
A partition $\lambda = (\lambda_1,\ldots,\lambda_n) \vdash n$ dominates a partition $\mu = (\mu_1,\ldots,\mu_n) \vdash n$ if $\sum_{i=1}^k (\lambda_i - \mu_i) \geq 0$ for all $k$.

Code

def statistic(L):
    return len(L.dominated_partitions())

Created

Dec 08, 2015 at 16:23 by Christian Stump

Updated

Oct 29, 2017 at 20:53 by Martin Rubey