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Statistic identifier: St001204
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Collection: Dyck paths
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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 $S_{n-2}$.
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References: [1] Marczinzik, René Upper bounds for the dominant dimension of Nakayama and related algebras. [[zbMATH:06820683]]
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Code:
-----------------------------------------------------------------------------
Statistic values:
[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
-----------------------------------------------------------------------------
Created: May 15, 2018 at 22:34 by Rene Marczinzik
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Last Updated: May 15, 2018 at 22:34 by Rene Marczinzik