Identifier
-
Mp00080:
Set partitions
—to permutation⟶
Permutations
St000236: Permutations ⟶ ℤ
Values
=>
Cc0009;cc-rep-0
{{1}}=>[1]=>1
{{1,2}}=>[2,1]=>2
{{1},{2}}=>[1,2]=>2
{{1,2,3}}=>[2,3,1]=>3
{{1,2},{3}}=>[2,1,3]=>2
{{1,3},{2}}=>[3,2,1]=>2
{{1},{2,3}}=>[1,3,2]=>2
{{1},{2},{3}}=>[1,2,3]=>3
{{1,2,3,4}}=>[2,3,4,1]=>4
{{1,2,3},{4}}=>[2,3,1,4]=>3
{{1,2,4},{3}}=>[2,4,3,1]=>3
{{1,2},{3,4}}=>[2,1,4,3]=>2
{{1,2},{3},{4}}=>[2,1,3,4]=>3
{{1,3,4},{2}}=>[3,2,4,1]=>3
{{1,3},{2,4}}=>[3,4,1,2]=>0
{{1,3},{2},{4}}=>[3,2,1,4]=>2
{{1,4},{2,3}}=>[4,3,2,1]=>2
{{1},{2,3,4}}=>[1,3,4,2]=>3
{{1},{2,3},{4}}=>[1,3,2,4]=>3
{{1,4},{2},{3}}=>[4,2,3,1]=>3
{{1},{2,4},{3}}=>[1,4,3,2]=>2
{{1},{2},{3,4}}=>[1,2,4,3]=>3
{{1},{2},{3},{4}}=>[1,2,3,4]=>4
{{1,2,3,4,5}}=>[2,3,4,5,1]=>5
{{1,2,3,4},{5}}=>[2,3,4,1,5]=>4
{{1,2,3,5},{4}}=>[2,3,5,4,1]=>4
{{1,2,3},{4,5}}=>[2,3,1,5,4]=>3
{{1,2,3},{4},{5}}=>[2,3,1,4,5]=>4
{{1,2,4,5},{3}}=>[2,4,3,5,1]=>4
{{1,2,4},{3,5}}=>[2,4,5,1,3]=>1
{{1,2,4},{3},{5}}=>[2,4,3,1,5]=>3
{{1,2,5},{3,4}}=>[2,5,4,3,1]=>3
{{1,2},{3,4,5}}=>[2,1,4,5,3]=>3
{{1,2},{3,4},{5}}=>[2,1,4,3,5]=>3
{{1,2,5},{3},{4}}=>[2,5,3,4,1]=>4
{{1,2},{3,5},{4}}=>[2,1,5,4,3]=>2
{{1,2},{3},{4,5}}=>[2,1,3,5,4]=>3
{{1,2},{3},{4},{5}}=>[2,1,3,4,5]=>4
{{1,3,4,5},{2}}=>[3,2,4,5,1]=>4
{{1,3,4},{2,5}}=>[3,5,4,1,2]=>1
{{1,3,4},{2},{5}}=>[3,2,4,1,5]=>3
{{1,3,5},{2,4}}=>[3,4,5,2,1]=>1
{{1,3},{2,4,5}}=>[3,4,1,5,2]=>1
{{1,3},{2,4},{5}}=>[3,4,1,2,5]=>1
{{1,3,5},{2},{4}}=>[3,2,5,4,1]=>3
{{1,3},{2,5},{4}}=>[3,5,1,4,2]=>1
{{1,3},{2},{4,5}}=>[3,2,1,5,4]=>2
{{1,3},{2},{4},{5}}=>[3,2,1,4,5]=>3
{{1,4,5},{2,3}}=>[4,3,2,5,1]=>3
{{1,4},{2,3,5}}=>[4,3,5,1,2]=>1
{{1,4},{2,3},{5}}=>[4,3,2,1,5]=>2
{{1,5},{2,3,4}}=>[5,3,4,2,1]=>3
{{1},{2,3,4,5}}=>[1,3,4,5,2]=>4
{{1},{2,3,4},{5}}=>[1,3,4,2,5]=>4
{{1,5},{2,3},{4}}=>[5,3,2,4,1]=>3
{{1},{2,3,5},{4}}=>[1,3,5,4,2]=>3
{{1},{2,3},{4,5}}=>[1,3,2,5,4]=>3
{{1},{2,3},{4},{5}}=>[1,3,2,4,5]=>4
{{1,4,5},{2},{3}}=>[4,2,3,5,1]=>4
{{1,4},{2,5},{3}}=>[4,5,3,1,2]=>1
{{1,4},{2},{3,5}}=>[4,2,5,1,3]=>1
{{1,4},{2},{3},{5}}=>[4,2,3,1,5]=>3
{{1,5},{2,4},{3}}=>[5,4,3,2,1]=>2
{{1},{2,4,5},{3}}=>[1,4,3,5,2]=>3
{{1},{2,4},{3,5}}=>[1,4,5,2,3]=>1
{{1},{2,4},{3},{5}}=>[1,4,3,2,5]=>3
{{1,5},{2},{3,4}}=>[5,2,4,3,1]=>3
{{1},{2,5},{3,4}}=>[1,5,4,3,2]=>2
{{1},{2},{3,4,5}}=>[1,2,4,5,3]=>4
{{1},{2},{3,4},{5}}=>[1,2,4,3,5]=>4
{{1,5},{2},{3},{4}}=>[5,2,3,4,1]=>4
{{1},{2,5},{3},{4}}=>[1,5,3,4,2]=>3
{{1},{2},{3,5},{4}}=>[1,2,5,4,3]=>3
{{1},{2},{3},{4,5}}=>[1,2,3,5,4]=>4
{{1},{2},{3},{4},{5}}=>[1,2,3,4,5]=>5
{{1,2,3,4,5,6}}=>[2,3,4,5,6,1]=>6
{{1,2,3,4,5},{6}}=>[2,3,4,5,1,6]=>5
{{1,2,3,4,6},{5}}=>[2,3,4,6,5,1]=>5
{{1,2,3,4},{5,6}}=>[2,3,4,1,6,5]=>4
{{1,2,3,4},{5},{6}}=>[2,3,4,1,5,6]=>5
{{1,2,3,5,6},{4}}=>[2,3,5,4,6,1]=>5
{{1,2,3,5},{4,6}}=>[2,3,5,6,1,4]=>2
{{1,2,3,5},{4},{6}}=>[2,3,5,4,1,6]=>4
{{1,2,3,6},{4,5}}=>[2,3,6,5,4,1]=>4
{{1,2,3},{4,5,6}}=>[2,3,1,5,6,4]=>4
{{1,2,3},{4,5},{6}}=>[2,3,1,5,4,6]=>4
{{1,2,3,6},{4},{5}}=>[2,3,6,4,5,1]=>5
{{1,2,3},{4,6},{5}}=>[2,3,1,6,5,4]=>3
{{1,2,3},{4},{5,6}}=>[2,3,1,4,6,5]=>4
{{1,2,3},{4},{5},{6}}=>[2,3,1,4,5,6]=>5
{{1,2,4,5,6},{3}}=>[2,4,3,5,6,1]=>5
{{1,2,4,5},{3,6}}=>[2,4,6,5,1,3]=>2
{{1,2,4,5},{3},{6}}=>[2,4,3,5,1,6]=>4
{{1,2,4,6},{3,5}}=>[2,4,5,6,3,1]=>2
{{1,2,4},{3,5,6}}=>[2,4,5,1,6,3]=>2
{{1,2,4},{3,5},{6}}=>[2,4,5,1,3,6]=>2
{{1,2,4,6},{3},{5}}=>[2,4,3,6,5,1]=>4
{{1,2,4},{3,6},{5}}=>[2,4,6,1,5,3]=>2
{{1,2,4},{3},{5,6}}=>[2,4,3,1,6,5]=>3
{{1,2,4},{3},{5},{6}}=>[2,4,3,1,5,6]=>4
{{1,2,5,6},{3,4}}=>[2,5,4,3,6,1]=>4
{{1,2,5},{3,4,6}}=>[2,5,4,6,1,3]=>2
{{1,2,5},{3,4},{6}}=>[2,5,4,3,1,6]=>3
{{1,2,6},{3,4,5}}=>[2,6,4,5,3,1]=>4
{{1,2},{3,4,5,6}}=>[2,1,4,5,6,3]=>4
{{1,2},{3,4,5},{6}}=>[2,1,4,5,3,6]=>4
{{1,2,6},{3,4},{5}}=>[2,6,4,3,5,1]=>4
{{1,2},{3,4,6},{5}}=>[2,1,4,6,5,3]=>3
{{1,2},{3,4},{5,6}}=>[2,1,4,3,6,5]=>3
{{1,2},{3,4},{5},{6}}=>[2,1,4,3,5,6]=>4
{{1,2,5,6},{3},{4}}=>[2,5,3,4,6,1]=>5
{{1,2,5},{3,6},{4}}=>[2,5,6,4,1,3]=>2
{{1,2,5},{3},{4,6}}=>[2,5,3,6,1,4]=>2
{{1,2,5},{3},{4},{6}}=>[2,5,3,4,1,6]=>4
{{1,2,6},{3,5},{4}}=>[2,6,5,4,3,1]=>3
{{1,2},{3,5,6},{4}}=>[2,1,5,4,6,3]=>3
{{1,2},{3,5},{4,6}}=>[2,1,5,6,3,4]=>1
{{1,2},{3,5},{4},{6}}=>[2,1,5,4,3,6]=>3
{{1,2,6},{3},{4,5}}=>[2,6,3,5,4,1]=>4
{{1,2},{3,6},{4,5}}=>[2,1,6,5,4,3]=>2
{{1,2},{3},{4,5,6}}=>[2,1,3,5,6,4]=>4
{{1,2},{3},{4,5},{6}}=>[2,1,3,5,4,6]=>4
{{1,2,6},{3},{4},{5}}=>[2,6,3,4,5,1]=>5
{{1,2},{3,6},{4},{5}}=>[2,1,6,4,5,3]=>3
{{1,2},{3},{4,6},{5}}=>[2,1,3,6,5,4]=>3
{{1,2},{3},{4},{5,6}}=>[2,1,3,4,6,5]=>4
{{1,2},{3},{4},{5},{6}}=>[2,1,3,4,5,6]=>5
{{1,3,4,5,6},{2}}=>[3,2,4,5,6,1]=>5
{{1,3,4,5},{2,6}}=>[3,6,4,5,1,2]=>2
{{1,3,4,5},{2},{6}}=>[3,2,4,5,1,6]=>4
{{1,3,4,6},{2,5}}=>[3,5,4,6,2,1]=>2
{{1,3,4},{2,5,6}}=>[3,5,4,1,6,2]=>2
{{1,3,4},{2,5},{6}}=>[3,5,4,1,2,6]=>2
{{1,3,4,6},{2},{5}}=>[3,2,4,6,5,1]=>4
{{1,3,4},{2,6},{5}}=>[3,6,4,1,5,2]=>2
{{1,3,4},{2},{5,6}}=>[3,2,4,1,6,5]=>3
{{1,3,4},{2},{5},{6}}=>[3,2,4,1,5,6]=>4
{{1,3,5,6},{2,4}}=>[3,4,5,2,6,1]=>2
{{1,3,5},{2,4,6}}=>[3,4,5,6,1,2]=>0
{{1,3,5},{2,4},{6}}=>[3,4,5,2,1,6]=>1
{{1,3,6},{2,4,5}}=>[3,4,6,5,2,1]=>2
{{1,3},{2,4,5,6}}=>[3,4,1,5,6,2]=>2
{{1,3},{2,4,5},{6}}=>[3,4,1,5,2,6]=>2
{{1,3,6},{2,4},{5}}=>[3,4,6,2,5,1]=>2
{{1,3},{2,4,6},{5}}=>[3,4,1,6,5,2]=>1
{{1,3},{2,4},{5,6}}=>[3,4,1,2,6,5]=>1
{{1,3},{2,4},{5},{6}}=>[3,4,1,2,5,6]=>2
{{1,3,5,6},{2},{4}}=>[3,2,5,4,6,1]=>4
{{1,3,5},{2,6},{4}}=>[3,6,5,4,1,2]=>1
{{1,3,5},{2},{4,6}}=>[3,2,5,6,1,4]=>1
{{1,3,5},{2},{4},{6}}=>[3,2,5,4,1,6]=>3
{{1,3,6},{2,5},{4}}=>[3,5,6,4,2,1]=>2
{{1,3},{2,5,6},{4}}=>[3,5,1,4,6,2]=>2
{{1,3},{2,5},{4,6}}=>[3,5,1,6,2,4]=>0
{{1,3},{2,5},{4},{6}}=>[3,5,1,4,2,6]=>2
{{1,3,6},{2},{4,5}}=>[3,2,6,5,4,1]=>3
{{1,3},{2,6},{4,5}}=>[3,6,1,5,4,2]=>1
{{1,3},{2},{4,5,6}}=>[3,2,1,5,6,4]=>3
{{1,3},{2},{4,5},{6}}=>[3,2,1,5,4,6]=>3
{{1,3,6},{2},{4},{5}}=>[3,2,6,4,5,1]=>4
{{1,3},{2,6},{4},{5}}=>[3,6,1,4,5,2]=>2
{{1,3},{2},{4,6},{5}}=>[3,2,1,6,5,4]=>2
{{1,3},{2},{4},{5,6}}=>[3,2,1,4,6,5]=>3
{{1,3},{2},{4},{5},{6}}=>[3,2,1,4,5,6]=>4
{{1,4,5,6},{2,3}}=>[4,3,2,5,6,1]=>4
{{1,4,5},{2,3,6}}=>[4,3,6,5,1,2]=>2
{{1,4,5},{2,3},{6}}=>[4,3,2,5,1,6]=>3
{{1,4,6},{2,3,5}}=>[4,3,5,6,2,1]=>2
{{1,4},{2,3,5,6}}=>[4,3,5,1,6,2]=>2
{{1,4},{2,3,5},{6}}=>[4,3,5,1,2,6]=>2
{{1,4,6},{2,3},{5}}=>[4,3,2,6,5,1]=>3
{{1,4},{2,3,6},{5}}=>[4,3,6,1,5,2]=>2
{{1,4},{2,3},{5,6}}=>[4,3,2,1,6,5]=>2
{{1,4},{2,3},{5},{6}}=>[4,3,2,1,5,6]=>3
{{1,5,6},{2,3,4}}=>[5,3,4,2,6,1]=>4
{{1,5},{2,3,4,6}}=>[5,3,4,6,1,2]=>2
{{1,5},{2,3,4},{6}}=>[5,3,4,2,1,6]=>3
{{1,6},{2,3,4,5}}=>[6,3,4,5,2,1]=>4
{{1},{2,3,4,5,6}}=>[1,3,4,5,6,2]=>5
{{1},{2,3,4,5},{6}}=>[1,3,4,5,2,6]=>5
{{1,6},{2,3,4},{5}}=>[6,3,4,2,5,1]=>4
{{1},{2,3,4,6},{5}}=>[1,3,4,6,5,2]=>4
{{1},{2,3,4},{5,6}}=>[1,3,4,2,6,5]=>4
{{1},{2,3,4},{5},{6}}=>[1,3,4,2,5,6]=>5
{{1,5,6},{2,3},{4}}=>[5,3,2,4,6,1]=>4
{{1,5},{2,3,6},{4}}=>[5,3,6,4,1,2]=>2
{{1,5},{2,3},{4,6}}=>[5,3,2,6,1,4]=>1
{{1,5},{2,3},{4},{6}}=>[5,3,2,4,1,6]=>3
{{1,6},{2,3,5},{4}}=>[6,3,5,4,2,1]=>3
{{1},{2,3,5,6},{4}}=>[1,3,5,4,6,2]=>4
{{1},{2,3,5},{4,6}}=>[1,3,5,6,2,4]=>2
{{1},{2,3,5},{4},{6}}=>[1,3,5,4,2,6]=>4
{{1,6},{2,3},{4,5}}=>[6,3,2,5,4,1]=>3
{{1},{2,3,6},{4,5}}=>[1,3,6,5,4,2]=>3
{{1},{2,3},{4,5,6}}=>[1,3,2,5,6,4]=>4
{{1},{2,3},{4,5},{6}}=>[1,3,2,5,4,6]=>4
{{1,6},{2,3},{4},{5}}=>[6,3,2,4,5,1]=>4
{{1},{2,3,6},{4},{5}}=>[1,3,6,4,5,2]=>4
{{1},{2,3},{4,6},{5}}=>[1,3,2,6,5,4]=>3
{{1},{2,3},{4},{5,6}}=>[1,3,2,4,6,5]=>4
{{1},{2,3},{4},{5},{6}}=>[1,3,2,4,5,6]=>5
{{1,4,5,6},{2},{3}}=>[4,2,3,5,6,1]=>5
{{1,4,5},{2,6},{3}}=>[4,6,3,5,1,2]=>2
{{1,4,5},{2},{3,6}}=>[4,2,6,5,1,3]=>2
{{1,4,5},{2},{3},{6}}=>[4,2,3,5,1,6]=>4
{{1,4,6},{2,5},{3}}=>[4,5,3,6,2,1]=>2
{{1,4},{2,5,6},{3}}=>[4,5,3,1,6,2]=>2
{{1,4},{2,5},{3,6}}=>[4,5,6,1,2,3]=>0
{{1,4},{2,5},{3},{6}}=>[4,5,3,1,2,6]=>2
{{1,4,6},{2},{3,5}}=>[4,2,5,6,3,1]=>2
{{1,4},{2,6},{3,5}}=>[4,6,5,1,3,2]=>0
{{1,4},{2},{3,5,6}}=>[4,2,5,1,6,3]=>2
{{1,4},{2},{3,5},{6}}=>[4,2,5,1,3,6]=>2
{{1,4,6},{2},{3},{5}}=>[4,2,3,6,5,1]=>4
{{1,4},{2,6},{3},{5}}=>[4,6,3,1,5,2]=>2
{{1,4},{2},{3,6},{5}}=>[4,2,6,1,5,3]=>2
{{1,4},{2},{3},{5,6}}=>[4,2,3,1,6,5]=>3
{{1,4},{2},{3},{5},{6}}=>[4,2,3,1,5,6]=>4
{{1,5,6},{2,4},{3}}=>[5,4,3,2,6,1]=>3
{{1,5},{2,4,6},{3}}=>[5,4,3,6,1,2]=>1
{{1,5},{2,4},{3,6}}=>[5,4,6,2,1,3]=>0
{{1,5},{2,4},{3},{6}}=>[5,4,3,2,1,6]=>2
{{1,6},{2,4,5},{3}}=>[6,4,3,5,2,1]=>3
{{1},{2,4,5,6},{3}}=>[1,4,3,5,6,2]=>4
{{1},{2,4,5},{3,6}}=>[1,4,6,5,2,3]=>2
{{1},{2,4,5},{3},{6}}=>[1,4,3,5,2,6]=>4
{{1,6},{2,4},{3,5}}=>[6,4,5,2,3,1]=>1
{{1},{2,4,6},{3,5}}=>[1,4,5,6,3,2]=>1
{{1},{2,4},{3,5,6}}=>[1,4,5,2,6,3]=>2
{{1},{2,4},{3,5},{6}}=>[1,4,5,2,3,6]=>2
{{1,6},{2,4},{3},{5}}=>[6,4,3,2,5,1]=>3
{{1},{2,4,6},{3},{5}}=>[1,4,3,6,5,2]=>3
{{1},{2,4},{3,6},{5}}=>[1,4,6,2,5,3]=>2
{{1},{2,4},{3},{5,6}}=>[1,4,3,2,6,5]=>3
{{1},{2,4},{3},{5},{6}}=>[1,4,3,2,5,6]=>4
{{1,5,6},{2},{3,4}}=>[5,2,4,3,6,1]=>4
{{1,5},{2,6},{3,4}}=>[5,6,4,3,1,2]=>1
{{1,5},{2},{3,4,6}}=>[5,2,4,6,1,3]=>2
{{1,5},{2},{3,4},{6}}=>[5,2,4,3,1,6]=>3
{{1,6},{2,5},{3,4}}=>[6,5,4,3,2,1]=>2
{{1},{2,5,6},{3,4}}=>[1,5,4,3,6,2]=>3
{{1},{2,5},{3,4,6}}=>[1,5,4,6,2,3]=>2
{{1},{2,5},{3,4},{6}}=>[1,5,4,3,2,6]=>3
{{1,6},{2},{3,4,5}}=>[6,2,4,5,3,1]=>4
{{1},{2,6},{3,4,5}}=>[1,6,4,5,3,2]=>3
{{1},{2},{3,4,5,6}}=>[1,2,4,5,6,3]=>5
{{1},{2},{3,4,5},{6}}=>[1,2,4,5,3,6]=>5
{{1,6},{2},{3,4},{5}}=>[6,2,4,3,5,1]=>4
{{1},{2,6},{3,4},{5}}=>[1,6,4,3,5,2]=>3
{{1},{2},{3,4,6},{5}}=>[1,2,4,6,5,3]=>4
{{1},{2},{3,4},{5,6}}=>[1,2,4,3,6,5]=>4
{{1},{2},{3,4},{5},{6}}=>[1,2,4,3,5,6]=>5
{{1,5,6},{2},{3},{4}}=>[5,2,3,4,6,1]=>5
{{1,5},{2,6},{3},{4}}=>[5,6,3,4,1,2]=>2
{{1,5},{2},{3,6},{4}}=>[5,2,6,4,1,3]=>2
{{1,5},{2},{3},{4,6}}=>[5,2,3,6,1,4]=>2
{{1,5},{2},{3},{4},{6}}=>[5,2,3,4,1,6]=>4
{{1,6},{2,5},{3},{4}}=>[6,5,3,4,2,1]=>3
{{1},{2,5,6},{3},{4}}=>[1,5,3,4,6,2]=>4
{{1},{2,5},{3,6},{4}}=>[1,5,6,4,2,3]=>2
{{1},{2,5},{3},{4,6}}=>[1,5,3,6,2,4]=>2
{{1},{2,5},{3},{4},{6}}=>[1,5,3,4,2,6]=>4
{{1,6},{2},{3,5},{4}}=>[6,2,5,4,3,1]=>3
{{1},{2,6},{3,5},{4}}=>[1,6,5,4,3,2]=>2
{{1},{2},{3,5,6},{4}}=>[1,2,5,4,6,3]=>4
{{1},{2},{3,5},{4,6}}=>[1,2,5,6,3,4]=>2
{{1},{2},{3,5},{4},{6}}=>[1,2,5,4,3,6]=>4
{{1,6},{2},{3},{4,5}}=>[6,2,3,5,4,1]=>4
{{1},{2,6},{3},{4,5}}=>[1,6,3,5,4,2]=>3
{{1},{2},{3,6},{4,5}}=>[1,2,6,5,4,3]=>3
{{1},{2},{3},{4,5,6}}=>[1,2,3,5,6,4]=>5
{{1},{2},{3},{4,5},{6}}=>[1,2,3,5,4,6]=>5
{{1,6},{2},{3},{4},{5}}=>[6,2,3,4,5,1]=>5
{{1},{2,6},{3},{4},{5}}=>[1,6,3,4,5,2]=>4
{{1},{2},{3,6},{4},{5}}=>[1,2,6,4,5,3]=>4
{{1},{2},{3},{4,6},{5}}=>[1,2,3,6,5,4]=>4
{{1},{2},{3},{4},{5,6}}=>[1,2,3,4,6,5]=>5
{{1},{2},{3},{4},{5},{6}}=>[1,2,3,4,5,6]=>6
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Description
The number of cyclical small weak excedances.
A cyclical small weak excedance is an index $i$ such that $\pi_i \in \{ i,i+1 \}$ considered cyclically.
A cyclical small weak excedance is an index $i$ such that $\pi_i \in \{ i,i+1 \}$ considered cyclically.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
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