Processing math: 100%

Identifier
Values
[1] => [1] => [1,0,1,0] => [3,1,2] => 2
[2] => [2] => [1,1,0,0,1,0] => [2,4,1,3] => 2
[1,1] => [1,1] => [1,0,1,1,0,0] => [3,1,4,2] => 2
[3] => [2,1] => [1,0,1,0,1,0] => [4,1,2,3] => 3
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searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Description
The Lowey length of the algebra A/T when T is the 1-tilting module corresponding to the permutation in the Auslander algebra of K[x]/(xn).
Map
2-conjugate
Description
Return a partition with the same number of odd parts and number of even parts interchanged with the number of cells with zero leg and odd arm length.
This is a special case of an involution that preserves the sequence of non-zero remainders of the parts under division by s and interchanges the number of parts divisible by s and the number of cells with zero leg length and arm length congruent to s−1 modulo s.
In particular, for s=1 the involution is conjugation, hence the name.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.