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Statistic identifier: St001491
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Collection: Binary words
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Description: The number of indecomposable projective-injective modules in the algebra corresponding to a subset.
Let $A_n=K[x]/(x^n)$.
We associate to a nonempty subset S of an (n-1)-set the module $M_S$, which is the direct sum of $A_n$-modules with indecomposable non-projective direct summands of dimension $i$ when $i$ is in $S$ (note that such modules have vector space dimension at most n-1). Then the corresponding algebra associated to S is the stable endomorphism ring of $M_S$. We decode the subset as a binary word so that for example the subset $S=\{1,3 \} $ of $\{1,2,3 \}$ is decoded as 101.
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References:
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Code:
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Statistic values:
1 => 1
01 => 1
10 => 1
11 => 2
001 => 1
010 => 1
011 => 1
100 => 1
101 => 2
110 => 1
111 => 3
0001 => 1
0010 => 1
0011 => 1
0100 => 1
0101 => 0
0110 => 2
0111 => 2
1000 => 1
1001 => 2
1010 => 0
1011 => 2
1100 => 1
1101 => 2
1110 => 2
1111 => 4
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Created: Nov 09, 2019 at 14:36 by Rene Marczinzik
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Last Updated: Nov 09, 2019 at 15:11 by Rene Marczinzik