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Statistic identifier: St001235

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Collection: Integer compositions

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Description: The global dimension of the corresponding Comp-Nakayama algebra.

We identify the composition [n1-1,n2-1,...,nr-1] with the Nakayama algebra with Kupisch series [n1,n1-1,...,2,n2,n2-1,...,2,...,nr,nr-1,...,3,2,1]. We call such Nakayama algebras with Kupisch series corresponding to a integer composition "Comp-Nakayama algebra".

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References: 

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Code:


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Statistic values:

[1]           => 1
[1,1]         => 2
[2]           => 1
[1,1,1]       => 3
[1,2]         => 2
[2,1]         => 2
[3]           => 1
[1,1,1,1]     => 4
[1,1,2]       => 3
[1,2,1]       => 2
[1,3]         => 2
[2,1,1]       => 3
[2,2]         => 2
[3,1]         => 2
[4]           => 1
[1,1,1,1,1]   => 5
[1,1,1,2]     => 4
[1,1,2,1]     => 3
[1,1,3]       => 3
[1,2,1,1]     => 3
[1,2,2]       => 2
[1,3,1]       => 2
[1,4]         => 2
[2,1,1,1]     => 4
[2,1,2]       => 3
[2,2,1]       => 2
[2,3]         => 2
[3,1,1]       => 3
[3,2]         => 2
[4,1]         => 2
[5]           => 1
[1,1,1,1,1,1] => 6
[1,1,1,1,2]   => 5
[1,1,1,2,1]   => 4
[1,1,1,3]     => 4
[1,1,2,1,1]   => 3
[1,1,2,2]     => 3
[1,1,3,1]     => 3
[1,1,4]       => 3
[1,2,1,1,1]   => 4
[1,2,1,2]     => 3
[1,2,2,1]     => 2
[1,2,3]       => 2
[1,3,1,1]     => 3
[1,3,2]       => 2
[1,4,1]       => 2
[1,5]         => 2
[2,1,1,1,1]   => 5
[2,1,1,2]     => 4
[2,1,2,1]     => 3
[2,1,3]       => 3
[2,2,1,1]     => 3
[2,2,2]       => 2
[2,3,1]       => 2
[2,4]         => 2
[3,1,1,1]     => 4
[3,1,2]       => 3
[3,2,1]       => 2
[3,3]         => 2
[4,1,1]       => 3
[4,2]         => 2
[5,1]         => 2
[6]           => 1

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Created: Jul 30, 2018 at 20:58 by Rene Marczinzik

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Last Updated: Jul 30, 2018 at 20:58 by Rene Marczinzik