Identifier
- St000230: Set partitions ⟶ ℤ
Values
=>
Cc0009;cc-rep
{{1}}=>1
{{1,2}}=>1
{{1},{2}}=>3
{{1,2,3}}=>1
{{1,2},{3}}=>4
{{1,3},{2}}=>3
{{1},{2,3}}=>3
{{1},{2},{3}}=>6
{{1,2,3,4}}=>1
{{1,2,3},{4}}=>5
{{1,2,4},{3}}=>4
{{1,2},{3,4}}=>4
{{1,2},{3},{4}}=>8
{{1,3,4},{2}}=>3
{{1,3},{2,4}}=>3
{{1,3},{2},{4}}=>7
{{1,4},{2,3}}=>3
{{1},{2,3,4}}=>3
{{1},{2,3},{4}}=>7
{{1,4},{2},{3}}=>6
{{1},{2,4},{3}}=>6
{{1},{2},{3,4}}=>6
{{1},{2},{3},{4}}=>10
{{1,2,3,4,5}}=>1
{{1,2,3,4},{5}}=>6
{{1,2,3,5},{4}}=>5
{{1,2,3},{4,5}}=>5
{{1,2,3},{4},{5}}=>10
{{1,2,4,5},{3}}=>4
{{1,2,4},{3,5}}=>4
{{1,2,4},{3},{5}}=>9
{{1,2,5},{3,4}}=>4
{{1,2},{3,4,5}}=>4
{{1,2},{3,4},{5}}=>9
{{1,2,5},{3},{4}}=>8
{{1,2},{3,5},{4}}=>8
{{1,2},{3},{4,5}}=>8
{{1,2},{3},{4},{5}}=>13
{{1,3,4,5},{2}}=>3
{{1,3,4},{2,5}}=>3
{{1,3,4},{2},{5}}=>8
{{1,3,5},{2,4}}=>3
{{1,3},{2,4,5}}=>3
{{1,3},{2,4},{5}}=>8
{{1,3,5},{2},{4}}=>7
{{1,3},{2,5},{4}}=>7
{{1,3},{2},{4,5}}=>7
{{1,3},{2},{4},{5}}=>12
{{1,4,5},{2,3}}=>3
{{1,4},{2,3,5}}=>3
{{1,4},{2,3},{5}}=>8
{{1,5},{2,3,4}}=>3
{{1},{2,3,4,5}}=>3
{{1},{2,3,4},{5}}=>8
{{1,5},{2,3},{4}}=>7
{{1},{2,3,5},{4}}=>7
{{1},{2,3},{4,5}}=>7
{{1},{2,3},{4},{5}}=>12
{{1,4,5},{2},{3}}=>6
{{1,4},{2,5},{3}}=>6
{{1,4},{2},{3,5}}=>6
{{1,4},{2},{3},{5}}=>11
{{1,5},{2,4},{3}}=>6
{{1},{2,4,5},{3}}=>6
{{1},{2,4},{3,5}}=>6
{{1},{2,4},{3},{5}}=>11
{{1,5},{2},{3,4}}=>6
{{1},{2,5},{3,4}}=>6
{{1},{2},{3,4,5}}=>6
{{1},{2},{3,4},{5}}=>11
{{1,5},{2},{3},{4}}=>10
{{1},{2,5},{3},{4}}=>10
{{1},{2},{3,5},{4}}=>10
{{1},{2},{3},{4,5}}=>10
{{1},{2},{3},{4},{5}}=>15
{{1,2,3,4,5,6}}=>1
{{1,2,3,4,5},{6}}=>7
{{1,2,3,4,6},{5}}=>6
{{1,2,3,4},{5,6}}=>6
{{1,2,3,4},{5},{6}}=>12
{{1,2,3,5,6},{4}}=>5
{{1,2,3,5},{4,6}}=>5
{{1,2,3,5},{4},{6}}=>11
{{1,2,3,6},{4,5}}=>5
{{1,2,3},{4,5,6}}=>5
{{1,2,3},{4,5},{6}}=>11
{{1,2,3,6},{4},{5}}=>10
{{1,2,3},{4,6},{5}}=>10
{{1,2,3},{4},{5,6}}=>10
{{1,2,3},{4},{5},{6}}=>16
{{1,2,4,5,6},{3}}=>4
{{1,2,4,5},{3,6}}=>4
{{1,2,4,5},{3},{6}}=>10
{{1,2,4,6},{3,5}}=>4
{{1,2,4},{3,5,6}}=>4
{{1,2,4},{3,5},{6}}=>10
{{1,2,4,6},{3},{5}}=>9
{{1,2,4},{3,6},{5}}=>9
{{1,2,4},{3},{5,6}}=>9
{{1,2,4},{3},{5},{6}}=>15
{{1,2,5,6},{3,4}}=>4
{{1,2,5},{3,4,6}}=>4
{{1,2,5},{3,4},{6}}=>10
{{1,2,6},{3,4,5}}=>4
{{1,2},{3,4,5,6}}=>4
{{1,2},{3,4,5},{6}}=>10
{{1,2,6},{3,4},{5}}=>9
{{1,2},{3,4,6},{5}}=>9
{{1,2},{3,4},{5,6}}=>9
{{1,2},{3,4},{5},{6}}=>15
{{1,2,5,6},{3},{4}}=>8
{{1,2,5},{3,6},{4}}=>8
{{1,2,5},{3},{4,6}}=>8
{{1,2,5},{3},{4},{6}}=>14
{{1,2,6},{3,5},{4}}=>8
{{1,2},{3,5,6},{4}}=>8
{{1,2},{3,5},{4,6}}=>8
{{1,2},{3,5},{4},{6}}=>14
{{1,2,6},{3},{4,5}}=>8
{{1,2},{3,6},{4,5}}=>8
{{1,2},{3},{4,5,6}}=>8
{{1,2},{3},{4,5},{6}}=>14
{{1,2,6},{3},{4},{5}}=>13
{{1,2},{3,6},{4},{5}}=>13
{{1,2},{3},{4,6},{5}}=>13
{{1,2},{3},{4},{5,6}}=>13
{{1,2},{3},{4},{5},{6}}=>19
{{1,3,4,5,6},{2}}=>3
{{1,3,4,5},{2,6}}=>3
{{1,3,4,5},{2},{6}}=>9
{{1,3,4,6},{2,5}}=>3
{{1,3,4},{2,5,6}}=>3
{{1,3,4},{2,5},{6}}=>9
{{1,3,4,6},{2},{5}}=>8
{{1,3,4},{2,6},{5}}=>8
{{1,3,4},{2},{5,6}}=>8
{{1,3,4},{2},{5},{6}}=>14
{{1,3,5,6},{2,4}}=>3
{{1,3,5},{2,4,6}}=>3
{{1,3,5},{2,4},{6}}=>9
{{1,3,6},{2,4,5}}=>3
{{1,3},{2,4,5,6}}=>3
{{1,3},{2,4,5},{6}}=>9
{{1,3,6},{2,4},{5}}=>8
{{1,3},{2,4,6},{5}}=>8
{{1,3},{2,4},{5,6}}=>8
{{1,3},{2,4},{5},{6}}=>14
{{1,3,5,6},{2},{4}}=>7
{{1,3,5},{2,6},{4}}=>7
{{1,3,5},{2},{4,6}}=>7
{{1,3,5},{2},{4},{6}}=>13
{{1,3,6},{2,5},{4}}=>7
{{1,3},{2,5,6},{4}}=>7
{{1,3},{2,5},{4,6}}=>7
{{1,3},{2,5},{4},{6}}=>13
{{1,3,6},{2},{4,5}}=>7
{{1,3},{2,6},{4,5}}=>7
{{1,3},{2},{4,5,6}}=>7
{{1,3},{2},{4,5},{6}}=>13
{{1,3,6},{2},{4},{5}}=>12
{{1,3},{2,6},{4},{5}}=>12
{{1,3},{2},{4,6},{5}}=>12
{{1,3},{2},{4},{5,6}}=>12
{{1,3},{2},{4},{5},{6}}=>18
{{1,4,5,6},{2,3}}=>3
{{1,4,5},{2,3,6}}=>3
{{1,4,5},{2,3},{6}}=>9
{{1,4,6},{2,3,5}}=>3
{{1,4},{2,3,5,6}}=>3
{{1,4},{2,3,5},{6}}=>9
{{1,4,6},{2,3},{5}}=>8
{{1,4},{2,3,6},{5}}=>8
{{1,4},{2,3},{5,6}}=>8
{{1,4},{2,3},{5},{6}}=>14
{{1,5,6},{2,3,4}}=>3
{{1,5},{2,3,4,6}}=>3
{{1,5},{2,3,4},{6}}=>9
{{1,6},{2,3,4,5}}=>3
{{1},{2,3,4,5,6}}=>3
{{1},{2,3,4,5},{6}}=>9
{{1,6},{2,3,4},{5}}=>8
{{1},{2,3,4,6},{5}}=>8
{{1},{2,3,4},{5,6}}=>8
{{1},{2,3,4},{5},{6}}=>14
{{1,5,6},{2,3},{4}}=>7
{{1,5},{2,3,6},{4}}=>7
{{1,5},{2,3},{4,6}}=>7
{{1,5},{2,3},{4},{6}}=>13
{{1,6},{2,3,5},{4}}=>7
{{1},{2,3,5,6},{4}}=>7
{{1},{2,3,5},{4,6}}=>7
{{1},{2,3,5},{4},{6}}=>13
{{1,6},{2,3},{4,5}}=>7
{{1},{2,3,6},{4,5}}=>7
{{1},{2,3},{4,5,6}}=>7
{{1},{2,3},{4,5},{6}}=>13
{{1,6},{2,3},{4},{5}}=>12
{{1},{2,3,6},{4},{5}}=>12
{{1},{2,3},{4,6},{5}}=>12
{{1},{2,3},{4},{5,6}}=>12
{{1},{2,3},{4},{5},{6}}=>18
{{1,4,5,6},{2},{3}}=>6
{{1,4,5},{2,6},{3}}=>6
{{1,4,5},{2},{3,6}}=>6
{{1,4,5},{2},{3},{6}}=>12
{{1,4,6},{2,5},{3}}=>6
{{1,4},{2,5,6},{3}}=>6
{{1,4},{2,5},{3,6}}=>6
{{1,4},{2,5},{3},{6}}=>12
{{1,4,6},{2},{3,5}}=>6
{{1,4},{2,6},{3,5}}=>6
{{1,4},{2},{3,5,6}}=>6
{{1,4},{2},{3,5},{6}}=>12
{{1,4,6},{2},{3},{5}}=>11
{{1,4},{2,6},{3},{5}}=>11
{{1,4},{2},{3,6},{5}}=>11
{{1,4},{2},{3},{5,6}}=>11
{{1,4},{2},{3},{5},{6}}=>17
{{1,5,6},{2,4},{3}}=>6
{{1,5},{2,4,6},{3}}=>6
{{1,5},{2,4},{3,6}}=>6
{{1,5},{2,4},{3},{6}}=>12
{{1,6},{2,4,5},{3}}=>6
{{1},{2,4,5,6},{3}}=>6
{{1},{2,4,5},{3,6}}=>6
{{1},{2,4,5},{3},{6}}=>12
{{1,6},{2,4},{3,5}}=>6
{{1},{2,4,6},{3,5}}=>6
{{1},{2,4},{3,5,6}}=>6
{{1},{2,4},{3,5},{6}}=>12
{{1,6},{2,4},{3},{5}}=>11
{{1},{2,4,6},{3},{5}}=>11
{{1},{2,4},{3,6},{5}}=>11
{{1},{2,4},{3},{5,6}}=>11
{{1},{2,4},{3},{5},{6}}=>17
{{1,5,6},{2},{3,4}}=>6
{{1,5},{2,6},{3,4}}=>6
{{1,5},{2},{3,4,6}}=>6
{{1,5},{2},{3,4},{6}}=>12
{{1,6},{2,5},{3,4}}=>6
{{1},{2,5,6},{3,4}}=>6
{{1},{2,5},{3,4,6}}=>6
{{1},{2,5},{3,4},{6}}=>12
{{1,6},{2},{3,4,5}}=>6
{{1},{2,6},{3,4,5}}=>6
{{1},{2},{3,4,5,6}}=>6
{{1},{2},{3,4,5},{6}}=>12
{{1,6},{2},{3,4},{5}}=>11
{{1},{2,6},{3,4},{5}}=>11
{{1},{2},{3,4,6},{5}}=>11
{{1},{2},{3,4},{5,6}}=>11
{{1},{2},{3,4},{5},{6}}=>17
{{1,5,6},{2},{3},{4}}=>10
{{1,5},{2,6},{3},{4}}=>10
{{1,5},{2},{3,6},{4}}=>10
{{1,5},{2},{3},{4,6}}=>10
{{1,5},{2},{3},{4},{6}}=>16
{{1,6},{2,5},{3},{4}}=>10
{{1},{2,5,6},{3},{4}}=>10
{{1},{2,5},{3,6},{4}}=>10
{{1},{2,5},{3},{4,6}}=>10
{{1},{2,5},{3},{4},{6}}=>16
{{1,6},{2},{3,5},{4}}=>10
{{1},{2,6},{3,5},{4}}=>10
{{1},{2},{3,5,6},{4}}=>10
{{1},{2},{3,5},{4,6}}=>10
{{1},{2},{3,5},{4},{6}}=>16
{{1,6},{2},{3},{4,5}}=>10
{{1},{2,6},{3},{4,5}}=>10
{{1},{2},{3,6},{4,5}}=>10
{{1},{2},{3},{4,5,6}}=>10
{{1},{2},{3},{4,5},{6}}=>16
{{1,6},{2},{3},{4},{5}}=>15
{{1},{2,6},{3},{4},{5}}=>15
{{1},{2},{3,6},{4},{5}}=>15
{{1},{2},{3},{4,6},{5}}=>15
{{1},{2},{3},{4},{5,6}}=>15
{{1},{2},{3},{4},{5},{6}}=>21
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Description
Sum of the minimal elements of the blocks of a set partition.
References
[1] Chern, B., Diaconis, P., Kane, D. M., Rhoades, R. C. Central Limit Theorems for some Set Partition Statistics arXiv:1502.00938
Code
def statistic(S):
return sum(min(B) for B in S)
Created
Feb 04, 2015 at 11:13 by Christian Stump
Updated
Oct 19, 2015 at 16:31 by Christian Stump
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