Identifier
Values
[1] => [1] => [1,0] => [2,1] => 4
[-1] => [1] => [1,0] => [2,1] => 4
[1,2] => [1,2] => [1,0,1,0] => [3,1,2] => 11
[1,-2] => [1,2] => [1,0,1,0] => [3,1,2] => 11
[-1,2] => [1,2] => [1,0,1,0] => [3,1,2] => 11
[-1,-2] => [1,2] => [1,0,1,0] => [3,1,2] => 11
[2,1] => [2,1] => [1,1,0,0] => [2,3,1] => 11
[2,-1] => [2,1] => [1,1,0,0] => [2,3,1] => 11
[-2,1] => [2,1] => [1,1,0,0] => [2,3,1] => 11
[-2,-1] => [2,1] => [1,1,0,0] => [2,3,1] => 11
[1,2,3] => [1,2,3] => [1,0,1,0,1,0] => [4,1,2,3] => 24
[1,2,-3] => [1,2,3] => [1,0,1,0,1,0] => [4,1,2,3] => 24
[1,-2,3] => [1,2,3] => [1,0,1,0,1,0] => [4,1,2,3] => 24
[1,-2,-3] => [1,2,3] => [1,0,1,0,1,0] => [4,1,2,3] => 24
[-1,2,3] => [1,2,3] => [1,0,1,0,1,0] => [4,1,2,3] => 24
[-1,2,-3] => [1,2,3] => [1,0,1,0,1,0] => [4,1,2,3] => 24
[-1,-2,3] => [1,2,3] => [1,0,1,0,1,0] => [4,1,2,3] => 24
[-1,-2,-3] => [1,2,3] => [1,0,1,0,1,0] => [4,1,2,3] => 24
[1,3,2] => [1,3,2] => [1,0,1,1,0,0] => [3,1,4,2] => 25
[1,3,-2] => [1,3,2] => [1,0,1,1,0,0] => [3,1,4,2] => 25
[1,-3,2] => [1,3,2] => [1,0,1,1,0,0] => [3,1,4,2] => 25
[1,-3,-2] => [1,3,2] => [1,0,1,1,0,0] => [3,1,4,2] => 25
[-1,3,2] => [1,3,2] => [1,0,1,1,0,0] => [3,1,4,2] => 25
[-1,3,-2] => [1,3,2] => [1,0,1,1,0,0] => [3,1,4,2] => 25
[-1,-3,2] => [1,3,2] => [1,0,1,1,0,0] => [3,1,4,2] => 25
[-1,-3,-2] => [1,3,2] => [1,0,1,1,0,0] => [3,1,4,2] => 25
[2,1,3] => [2,1,3] => [1,1,0,0,1,0] => [2,4,1,3] => 25
[2,1,-3] => [2,1,3] => [1,1,0,0,1,0] => [2,4,1,3] => 25
[2,-1,3] => [2,1,3] => [1,1,0,0,1,0] => [2,4,1,3] => 25
[2,-1,-3] => [2,1,3] => [1,1,0,0,1,0] => [2,4,1,3] => 25
[-2,1,3] => [2,1,3] => [1,1,0,0,1,0] => [2,4,1,3] => 25
[-2,1,-3] => [2,1,3] => [1,1,0,0,1,0] => [2,4,1,3] => 25
[-2,-1,3] => [2,1,3] => [1,1,0,0,1,0] => [2,4,1,3] => 25
[-2,-1,-3] => [2,1,3] => [1,1,0,0,1,0] => [2,4,1,3] => 25
[2,3,1] => [2,3,1] => [1,1,0,1,0,0] => [4,3,1,2] => 21
[2,3,-1] => [2,3,1] => [1,1,0,1,0,0] => [4,3,1,2] => 21
[2,-3,1] => [2,3,1] => [1,1,0,1,0,0] => [4,3,1,2] => 21
[2,-3,-1] => [2,3,1] => [1,1,0,1,0,0] => [4,3,1,2] => 21
[-2,3,1] => [2,3,1] => [1,1,0,1,0,0] => [4,3,1,2] => 21
[-2,3,-1] => [2,3,1] => [1,1,0,1,0,0] => [4,3,1,2] => 21
[-2,-3,1] => [2,3,1] => [1,1,0,1,0,0] => [4,3,1,2] => 21
[-2,-3,-1] => [2,3,1] => [1,1,0,1,0,0] => [4,3,1,2] => 21
[3,1,2] => [3,1,2] => [1,1,1,0,0,0] => [2,3,4,1] => 24
[3,1,-2] => [3,1,2] => [1,1,1,0,0,0] => [2,3,4,1] => 24
[3,-1,2] => [3,1,2] => [1,1,1,0,0,0] => [2,3,4,1] => 24
[3,-1,-2] => [3,1,2] => [1,1,1,0,0,0] => [2,3,4,1] => 24
[-3,1,2] => [3,1,2] => [1,1,1,0,0,0] => [2,3,4,1] => 24
[-3,1,-2] => [3,1,2] => [1,1,1,0,0,0] => [2,3,4,1] => 24
[-3,-1,2] => [3,1,2] => [1,1,1,0,0,0] => [2,3,4,1] => 24
[-3,-1,-2] => [3,1,2] => [1,1,1,0,0,0] => [2,3,4,1] => 24
[3,2,1] => [3,2,1] => [1,1,1,0,0,0] => [2,3,4,1] => 24
[3,2,-1] => [3,2,1] => [1,1,1,0,0,0] => [2,3,4,1] => 24
[3,-2,1] => [3,2,1] => [1,1,1,0,0,0] => [2,3,4,1] => 24
[3,-2,-1] => [3,2,1] => [1,1,1,0,0,0] => [2,3,4,1] => 24
[-3,2,1] => [3,2,1] => [1,1,1,0,0,0] => [2,3,4,1] => 24
[-3,2,-1] => [3,2,1] => [1,1,1,0,0,0] => [2,3,4,1] => 24
[-3,-2,1] => [3,2,1] => [1,1,1,0,0,0] => [2,3,4,1] => 24
[-3,-2,-1] => [3,2,1] => [1,1,1,0,0,0] => [2,3,4,1] => 24
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Description
The vector space dimension of the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
permutation
Description
The permutation obtained by forgetting the colours.