**Identifier**

Identifier

- St001491: Binary words ⟶ ℤ

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

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.

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**searching the database

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