Processing math: 100%

Identifier
Values
[1] => [1] => [1] => 0
[1,2] => [1,2] => [1,2] => 0
[2,1] => [1,2] => [1,2] => 0
[1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [1,3,2] => 0
[2,1,3] => [1,3,2] => [1,3,2] => 0
[2,3,1] => [1,2,3] => [1,2,3] => 0
[3,1,2] => [1,2,3] => [1,2,3] => 0
[3,2,1] => [1,2,3] => [1,2,3] => 0
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 0
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 0
[1,3,4,2] => [1,3,4,2] => [1,3,4,2] => 1
[1,4,2,3] => [1,4,2,3] => [1,4,2,3] => 0
[1,4,3,2] => [1,4,2,3] => [1,4,2,3] => 0
[2,1,3,4] => [1,3,4,2] => [1,3,4,2] => 1
[2,1,4,3] => [1,4,2,3] => [1,4,2,3] => 0
[2,3,1,4] => [1,4,2,3] => [1,4,2,3] => 0
[2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 0
[2,4,1,3] => [1,3,2,4] => [1,3,2,4] => 0
[2,4,3,1] => [1,2,4,3] => [1,2,4,3] => 0
[3,1,2,4] => [1,2,4,3] => [1,2,4,3] => 0
[3,1,4,2] => [1,4,2,3] => [1,4,2,3] => 0
[3,2,1,4] => [1,4,2,3] => [1,4,2,3] => 0
[3,2,4,1] => [1,2,4,3] => [1,2,4,3] => 0
[3,4,1,2] => [1,2,3,4] => [1,2,3,4] => 0
[3,4,2,1] => [1,2,3,4] => [1,2,3,4] => 0
[4,1,2,3] => [1,2,3,4] => [1,2,3,4] => 0
[4,1,3,2] => [1,3,2,4] => [1,3,2,4] => 0
[4,2,1,3] => [1,3,2,4] => [1,3,2,4] => 0
[4,2,3,1] => [1,2,3,4] => [1,2,3,4] => 0
[4,3,1,2] => [1,2,3,4] => [1,2,3,4] => 0
[4,3,2,1] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 0
[1,2,4,5,3] => [1,2,4,5,3] => [1,2,4,5,3] => 1
[1,2,5,3,4] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[1,2,5,4,3] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 0
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[1,3,4,2,5] => [1,3,4,2,5] => [1,3,4,2,5] => 1
[1,3,4,5,2] => [1,3,4,5,2] => [1,3,4,5,2] => 2
[1,3,5,2,4] => [1,3,5,2,4] => [1,3,5,2,4] => 1
[1,3,5,4,2] => [1,3,5,2,4] => [1,3,5,2,4] => 1
[1,4,2,3,5] => [1,4,2,3,5] => [1,4,2,3,5] => 0
[1,4,2,5,3] => [1,4,2,5,3] => [1,4,2,5,3] => 1
[1,4,3,2,5] => [1,4,2,5,3] => [1,4,2,5,3] => 1
[1,4,3,5,2] => [1,4,2,3,5] => [1,4,2,3,5] => 0
[1,4,5,2,3] => [1,4,5,2,3] => [1,4,5,2,3] => 1
[1,4,5,3,2] => [1,4,5,2,3] => [1,4,5,2,3] => 1
[1,5,2,3,4] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[1,5,2,4,3] => [1,5,2,4,3] => [1,5,2,4,3] => 0
[1,5,3,2,4] => [1,5,2,4,3] => [1,5,2,4,3] => 0
[1,5,3,4,2] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[1,5,4,2,3] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[1,5,4,3,2] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[2,1,3,4,5] => [1,3,4,5,2] => [1,3,4,5,2] => 2
[2,1,3,5,4] => [1,3,5,2,4] => [1,3,5,2,4] => 1
[2,1,4,3,5] => [1,4,2,3,5] => [1,4,2,3,5] => 0
[2,1,4,5,3] => [1,4,5,2,3] => [1,4,5,2,3] => 1
[2,1,5,3,4] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[2,1,5,4,3] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[2,3,1,4,5] => [1,4,5,2,3] => [1,4,5,2,3] => 1
[2,3,1,5,4] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[2,3,4,1,5] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[2,3,5,1,4] => [1,4,2,3,5] => [1,4,2,3,5] => 0
[2,3,5,4,1] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[2,4,1,3,5] => [1,3,5,2,4] => [1,3,5,2,4] => 1
[2,4,1,5,3] => [1,5,2,4,3] => [1,5,2,4,3] => 0
[2,4,3,1,5] => [1,5,2,4,3] => [1,5,2,4,3] => 0
[2,4,3,5,1] => [1,2,4,3,5] => [1,2,4,3,5] => 0
[2,4,5,1,3] => [1,3,2,4,5] => [1,3,2,4,5] => 0
[2,4,5,3,1] => [1,2,4,5,3] => [1,2,4,5,3] => 1
[2,5,1,3,4] => [1,3,4,2,5] => [1,3,4,2,5] => 1
[2,5,1,4,3] => [1,4,2,5,3] => [1,4,2,5,3] => 1
[2,5,3,1,4] => [1,4,2,5,3] => [1,4,2,5,3] => 1
[2,5,3,4,1] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[2,5,4,1,3] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[2,5,4,3,1] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[3,1,2,4,5] => [1,2,4,5,3] => [1,2,4,5,3] => 1
[3,1,2,5,4] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[3,1,4,2,5] => [1,4,2,5,3] => [1,4,2,5,3] => 1
[3,1,4,5,2] => [1,4,5,2,3] => [1,4,5,2,3] => 1
[3,1,5,2,4] => [1,5,2,4,3] => [1,5,2,4,3] => 0
[3,1,5,4,2] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[3,2,1,4,5] => [1,4,5,2,3] => [1,4,5,2,3] => 1
[3,2,1,5,4] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[3,2,4,1,5] => [1,5,2,4,3] => [1,5,2,4,3] => 0
[3,2,4,5,1] => [1,2,4,5,3] => [1,2,4,5,3] => 1
[3,2,5,1,4] => [1,4,2,5,3] => [1,4,2,5,3] => 1
[3,2,5,4,1] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[3,4,1,2,5] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[3,4,1,5,2] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[3,4,2,1,5] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[3,4,2,5,1] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[3,4,5,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[3,4,5,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[3,5,1,2,4] => [1,2,4,3,5] => [1,2,4,3,5] => 0
[3,5,1,4,2] => [1,4,2,3,5] => [1,4,2,3,5] => 0
>>> Load all 153 entries. <<<
[3,5,2,1,4] => [1,4,2,3,5] => [1,4,2,3,5] => 0
[3,5,2,4,1] => [1,2,4,3,5] => [1,2,4,3,5] => 0
[3,5,4,1,2] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[3,5,4,2,1] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[4,1,2,3,5] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[4,1,2,5,3] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[4,1,3,2,5] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[4,1,3,5,2] => [1,3,5,2,4] => [1,3,5,2,4] => 1
[4,1,5,2,3] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[4,1,5,3,2] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[4,2,1,3,5] => [1,3,5,2,4] => [1,3,5,2,4] => 1
[4,2,1,5,3] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[4,2,3,1,5] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[4,2,3,5,1] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[4,2,5,1,3] => [1,3,2,5,4] => [1,3,2,5,4] => 0
[4,2,5,3,1] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[4,3,1,2,5] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[4,3,1,5,2] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[4,3,2,1,5] => [1,5,2,3,4] => [1,5,2,3,4] => 0
[4,3,2,5,1] => [1,2,5,3,4] => [1,2,5,3,4] => 0
[4,3,5,1,2] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[4,3,5,2,1] => [1,2,3,5,4] => [1,2,3,5,4] => 0
[4,5,1,2,3] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[4,5,1,3,2] => [1,3,2,4,5] => [1,3,2,4,5] => 0
[4,5,2,1,3] => [1,3,2,4,5] => [1,3,2,4,5] => 0
[4,5,2,3,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[4,5,3,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[4,5,3,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,1,2,3,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,1,2,4,3] => [1,2,4,3,5] => [1,2,4,3,5] => 0
[5,1,3,2,4] => [1,3,2,4,5] => [1,3,2,4,5] => 0
[5,1,3,4,2] => [1,3,4,2,5] => [1,3,4,2,5] => 1
[5,1,4,2,3] => [1,4,2,3,5] => [1,4,2,3,5] => 0
[5,1,4,3,2] => [1,4,2,3,5] => [1,4,2,3,5] => 0
[5,2,1,3,4] => [1,3,4,2,5] => [1,3,4,2,5] => 1
[5,2,1,4,3] => [1,4,2,3,5] => [1,4,2,3,5] => 0
[5,2,3,1,4] => [1,4,2,3,5] => [1,4,2,3,5] => 0
[5,2,3,4,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,2,4,1,3] => [1,3,2,4,5] => [1,3,2,4,5] => 0
[5,2,4,3,1] => [1,2,4,3,5] => [1,2,4,3,5] => 0
[5,3,1,2,4] => [1,2,4,3,5] => [1,2,4,3,5] => 0
[5,3,1,4,2] => [1,4,2,3,5] => [1,4,2,3,5] => 0
[5,3,2,1,4] => [1,4,2,3,5] => [1,4,2,3,5] => 0
[5,3,2,4,1] => [1,2,4,3,5] => [1,2,4,3,5] => 0
[5,3,4,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,3,4,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,1,2,3] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,1,3,2] => [1,3,2,4,5] => [1,3,2,4,5] => 0
[5,4,2,1,3] => [1,3,2,4,5] => [1,3,2,4,5] => 0
[5,4,2,3,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,3,1,2] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[5,4,3,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
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Description
The number of occurrences of a type-B 231 pattern in a signed permutation.
For a signed permutation π∈Hn, a triple −n≤i<j<k≤n is an occurrence of the type-B 231 pattern, if 1≤j<k, π(i)<π(j) and π(i) is one larger than π(k), i.e., π(i)=π(k)+1 if π(k)≠−1 and π(i)=1 otherwise.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
Map
to signed permutation
Description
The signed permutation with all signs positive.