Identifier
- St001204: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[1,0,1,0]=>1
[1,1,0,0]=>0
[1,0,1,0,1,0]=>1
[1,0,1,1,0,0]=>1
[1,1,0,0,1,0]=>0
[1,1,0,1,0,0]=>0
[1,1,1,0,0,0]=>0
[1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,0]=>1
[1,1,0,0,1,0,1,0]=>0
[1,1,0,0,1,1,0,0]=>0
[1,1,0,1,0,0,1,0]=>0
[1,1,0,1,0,1,0,0]=>0
[1,1,0,1,1,0,0,0]=>0
[1,1,1,0,0,0,1,0]=>0
[1,1,1,0,0,1,0,0]=>0
[1,1,1,0,1,0,0,0]=>0
[1,1,1,1,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0]=>0
[1,1,0,0,1,0,1,1,0,0]=>0
[1,1,0,0,1,1,0,0,1,0]=>0
[1,1,0,0,1,1,0,1,0,0]=>0
[1,1,0,0,1,1,1,0,0,0]=>0
[1,1,0,1,0,0,1,0,1,0]=>0
[1,1,0,1,0,0,1,1,0,0]=>0
[1,1,0,1,0,1,0,0,1,0]=>0
[1,1,0,1,0,1,0,1,0,0]=>0
[1,1,0,1,0,1,1,0,0,0]=>0
[1,1,0,1,1,0,0,0,1,0]=>0
[1,1,0,1,1,0,0,1,0,0]=>0
[1,1,0,1,1,0,1,0,0,0]=>0
[1,1,0,1,1,1,0,0,0,0]=>0
[1,1,1,0,0,0,1,0,1,0]=>0
[1,1,1,0,0,0,1,1,0,0]=>0
[1,1,1,0,0,1,0,0,1,0]=>0
[1,1,1,0,0,1,0,1,0,0]=>0
[1,1,1,0,0,1,1,0,0,0]=>0
[1,1,1,0,1,0,0,0,1,0]=>0
[1,1,1,0,1,0,0,1,0,0]=>0
[1,1,1,0,1,0,1,0,0,0]=>0
[1,1,1,0,1,1,0,0,0,0]=>0
[1,1,1,1,0,0,0,0,1,0]=>0
[1,1,1,1,0,0,0,1,0,0]=>0
[1,1,1,1,0,0,1,0,0,0]=>0
[1,1,1,1,0,1,0,0,0,0]=>0
[1,1,1,1,1,0,0,0,0,0]=>0
[1,0,1,0,1,0,1,0,1,0,1,0]=>1
[1,0,1,0,1,0,1,0,1,1,0,0]=>1
[1,0,1,0,1,0,1,1,0,0,1,0]=>1
[1,0,1,0,1,0,1,1,0,1,0,0]=>1
[1,0,1,0,1,0,1,1,1,0,0,0]=>1
[1,0,1,0,1,1,0,0,1,0,1,0]=>1
[1,0,1,0,1,1,0,0,1,1,0,0]=>1
[1,0,1,0,1,1,0,1,0,0,1,0]=>1
[1,0,1,0,1,1,0,1,0,1,0,0]=>1
[1,0,1,0,1,1,0,1,1,0,0,0]=>1
[1,0,1,0,1,1,1,0,0,0,1,0]=>1
[1,0,1,0,1,1,1,0,0,1,0,0]=>1
[1,0,1,0,1,1,1,0,1,0,0,0]=>1
[1,0,1,0,1,1,1,1,0,0,0,0]=>1
[1,0,1,1,0,0,1,0,1,0,1,0]=>1
[1,0,1,1,0,0,1,0,1,1,0,0]=>1
[1,0,1,1,0,0,1,1,0,0,1,0]=>1
[1,0,1,1,0,0,1,1,0,1,0,0]=>1
[1,0,1,1,0,0,1,1,1,0,0,0]=>1
[1,0,1,1,0,1,0,0,1,0,1,0]=>1
[1,0,1,1,0,1,0,0,1,1,0,0]=>1
[1,0,1,1,0,1,0,1,0,0,1,0]=>1
[1,0,1,1,0,1,0,1,0,1,0,0]=>1
[1,0,1,1,0,1,0,1,1,0,0,0]=>1
[1,0,1,1,0,1,1,0,0,0,1,0]=>1
[1,0,1,1,0,1,1,0,0,1,0,0]=>1
[1,0,1,1,0,1,1,0,1,0,0,0]=>1
[1,0,1,1,0,1,1,1,0,0,0,0]=>1
[1,0,1,1,1,0,0,0,1,0,1,0]=>1
[1,0,1,1,1,0,0,0,1,1,0,0]=>1
[1,0,1,1,1,0,0,1,0,0,1,0]=>1
[1,0,1,1,1,0,0,1,0,1,0,0]=>1
[1,0,1,1,1,0,0,1,1,0,0,0]=>1
[1,0,1,1,1,0,1,0,0,0,1,0]=>1
[1,0,1,1,1,0,1,0,0,1,0,0]=>1
[1,0,1,1,1,0,1,0,1,0,0,0]=>1
[1,0,1,1,1,0,1,1,0,0,0,0]=>1
[1,0,1,1,1,1,0,0,0,0,1,0]=>1
[1,0,1,1,1,1,0,0,0,1,0,0]=>1
[1,0,1,1,1,1,0,0,1,0,0,0]=>1
[1,0,1,1,1,1,0,1,0,0,0,0]=>1
[1,0,1,1,1,1,1,0,0,0,0,0]=>1
[1,1,0,0,1,0,1,0,1,0,1,0]=>0
[1,1,0,0,1,0,1,0,1,1,0,0]=>0
[1,1,0,0,1,0,1,1,0,0,1,0]=>0
[1,1,0,0,1,0,1,1,0,1,0,0]=>0
[1,1,0,0,1,0,1,1,1,0,0,0]=>0
[1,1,0,0,1,1,0,0,1,0,1,0]=>0
[1,1,0,0,1,1,0,0,1,1,0,0]=>0
[1,1,0,0,1,1,0,1,0,0,1,0]=>0
[1,1,0,0,1,1,0,1,0,1,0,0]=>0
[1,1,0,0,1,1,0,1,1,0,0,0]=>0
[1,1,0,0,1,1,1,0,0,0,1,0]=>0
[1,1,0,0,1,1,1,0,0,1,0,0]=>0
[1,1,0,0,1,1,1,0,1,0,0,0]=>0
[1,1,0,0,1,1,1,1,0,0,0,0]=>0
[1,1,0,1,0,0,1,0,1,0,1,0]=>0
[1,1,0,1,0,0,1,0,1,1,0,0]=>0
[1,1,0,1,0,0,1,1,0,0,1,0]=>0
[1,1,0,1,0,0,1,1,0,1,0,0]=>0
[1,1,0,1,0,0,1,1,1,0,0,0]=>0
[1,1,0,1,0,1,0,0,1,0,1,0]=>0
[1,1,0,1,0,1,0,0,1,1,0,0]=>0
[1,1,0,1,0,1,0,1,0,0,1,0]=>0
[1,1,0,1,0,1,0,1,0,1,0,0]=>0
[1,1,0,1,0,1,0,1,1,0,0,0]=>0
[1,1,0,1,0,1,1,0,0,0,1,0]=>0
[1,1,0,1,0,1,1,0,0,1,0,0]=>0
[1,1,0,1,0,1,1,0,1,0,0,0]=>0
[1,1,0,1,0,1,1,1,0,0,0,0]=>0
[1,1,0,1,1,0,0,0,1,0,1,0]=>0
[1,1,0,1,1,0,0,0,1,1,0,0]=>0
[1,1,0,1,1,0,0,1,0,0,1,0]=>0
[1,1,0,1,1,0,0,1,0,1,0,0]=>0
[1,1,0,1,1,0,0,1,1,0,0,0]=>0
[1,1,0,1,1,0,1,0,0,0,1,0]=>0
[1,1,0,1,1,0,1,0,0,1,0,0]=>0
[1,1,0,1,1,0,1,0,1,0,0,0]=>0
[1,1,0,1,1,0,1,1,0,0,0,0]=>0
[1,1,0,1,1,1,0,0,0,0,1,0]=>0
[1,1,0,1,1,1,0,0,0,1,0,0]=>0
[1,1,0,1,1,1,0,0,1,0,0,0]=>0
[1,1,0,1,1,1,0,1,0,0,0,0]=>0
[1,1,0,1,1,1,1,0,0,0,0,0]=>0
[1,1,1,0,0,0,1,0,1,0,1,0]=>0
[1,1,1,0,0,0,1,0,1,1,0,0]=>0
[1,1,1,0,0,0,1,1,0,0,1,0]=>0
[1,1,1,0,0,0,1,1,0,1,0,0]=>0
[1,1,1,0,0,0,1,1,1,0,0,0]=>0
[1,1,1,0,0,1,0,0,1,0,1,0]=>0
[1,1,1,0,0,1,0,0,1,1,0,0]=>0
[1,1,1,0,0,1,0,1,0,0,1,0]=>0
[1,1,1,0,0,1,0,1,0,1,0,0]=>0
[1,1,1,0,0,1,0,1,1,0,0,0]=>0
[1,1,1,0,0,1,1,0,0,0,1,0]=>0
[1,1,1,0,0,1,1,0,0,1,0,0]=>0
[1,1,1,0,0,1,1,0,1,0,0,0]=>0
[1,1,1,0,0,1,1,1,0,0,0,0]=>0
[1,1,1,0,1,0,0,0,1,0,1,0]=>0
[1,1,1,0,1,0,0,0,1,1,0,0]=>0
[1,1,1,0,1,0,0,1,0,0,1,0]=>0
[1,1,1,0,1,0,0,1,0,1,0,0]=>0
[1,1,1,0,1,0,0,1,1,0,0,0]=>0
[1,1,1,0,1,0,1,0,0,0,1,0]=>0
[1,1,1,0,1,0,1,0,0,1,0,0]=>0
[1,1,1,0,1,0,1,0,1,0,0,0]=>0
[1,1,1,0,1,0,1,1,0,0,0,0]=>0
[1,1,1,0,1,1,0,0,0,0,1,0]=>0
[1,1,1,0,1,1,0,0,0,1,0,0]=>0
[1,1,1,0,1,1,0,0,1,0,0,0]=>0
[1,1,1,0,1,1,0,1,0,0,0,0]=>0
[1,1,1,0,1,1,1,0,0,0,0,0]=>0
[1,1,1,1,0,0,0,0,1,0,1,0]=>0
[1,1,1,1,0,0,0,0,1,1,0,0]=>0
[1,1,1,1,0,0,0,1,0,0,1,0]=>0
[1,1,1,1,0,0,0,1,0,1,0,0]=>0
[1,1,1,1,0,0,0,1,1,0,0,0]=>0
[1,1,1,1,0,0,1,0,0,0,1,0]=>0
[1,1,1,1,0,0,1,0,0,1,0,0]=>0
[1,1,1,1,0,0,1,0,1,0,0,0]=>0
[1,1,1,1,0,0,1,1,0,0,0,0]=>0
[1,1,1,1,0,1,0,0,0,0,1,0]=>0
[1,1,1,1,0,1,0,0,0,1,0,0]=>0
[1,1,1,1,0,1,0,0,1,0,0,0]=>0
[1,1,1,1,0,1,0,1,0,0,0,0]=>0
[1,1,1,1,0,1,1,0,0,0,0,0]=>0
[1,1,1,1,1,0,0,0,0,0,1,0]=>0
[1,1,1,1,1,0,0,0,0,1,0,0]=>0
[1,1,1,1,1,0,0,0,1,0,0,0]=>0
[1,1,1,1,1,0,0,1,0,0,0,0]=>0
[1,1,1,1,1,0,1,0,0,0,0,0]=>0
[1,1,1,1,1,1,0,0,0,0,0,0]=>0
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Description
Call a CNakayama algebra (a Nakayama algebra with a cyclic quiver) with Kupisch series $L=[c_0,c_1,...,c_{n−1}]$ such that $n=c_0 < c_i$ for all $i > 0$ a special CNakayama algebra.
Associate to this special CNakayama algebra a Dyck path as follows:
In the list L delete the first entry $c_0$ and substract from all other entries $n$−1 and then append the last element 1. The result is a Kupisch series of an LNakayama algebra.
The statistic gives the $(t-1)/2$ when $t$ is the projective dimension of the simple module $S_{n-2}$.
Associate to this special CNakayama algebra a Dyck path as follows:
In the list L delete the first entry $c_0$ and substract from all other entries $n$−1 and then append the last element 1. The result is a Kupisch series of an LNakayama algebra.
The statistic gives the $(t-1)/2$ when $t$ is the projective dimension of the simple module $S_{n-2}$.
References
[1] Marczinzik, René Upper bounds for the dominant dimension of Nakayama and related algebras. zbMATH:06820683
Created
May 15, 2018 at 22:34 by Rene Marczinzik
Updated
May 15, 2018 at 22:34 by Rene Marczinzik
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