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Identifier
Values
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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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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.
Created
Nov 09, 2019 at 14:36 by Rene Marczinzik
Updated
Nov 09, 2019 at 15:11 by Rene Marczinzik