Algebras associated to acyclic directed graphs

Vladimir Retakh; Robert Lee Wilson

doi:10.1016/j.aam.2008.04.002

Algebras associated to acyclic directed graphs

Vladimir Retakh, Robert Lee Wilson

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices and edges. Each finite acyclic directed graph admits countably many structures of a generalized layered graph. We construct linear bases in such algebras and compute their Hilbert series. Our interest to generalized layered graphs and algebras associated to those graphs is motivated by their relations to factorizations of polynomials over noncommutative rings.

Original language	English (US)
Pages (from-to)	42-59
Number of pages	18
Journal	Advances in Applied Mathematics
Volume	42
Issue number	1
DOIs	https://doi.org/10.1016/j.aam.2008.04.002
State	Published - Jan 2009

All Science Journal Classification (ASJC) codes

Applied Mathematics

Keywords

Factorizations of noncommutative polynomials
Generalized layered graphs
Hilbert series

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10.1016/j.aam.2008.04.002

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title = "Algebras associated to acyclic directed graphs",

abstract = "We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices and edges. Each finite acyclic directed graph admits countably many structures of a generalized layered graph. We construct linear bases in such algebras and compute their Hilbert series. Our interest to generalized layered graphs and algebras associated to those graphs is motivated by their relations to factorizations of polynomials over noncommutative rings.",

keywords = "Factorizations of noncommutative polynomials, Generalized layered graphs, Hilbert series",

author = "Vladimir Retakh and Wilson, {Robert Lee}",

note = "Funding Information: States. E-mail addresses: vretakh@math.rutgers.edu (V. Retakh), rwilson@math.rutgers.edu (R.L. Wilson). 1 Both authors were supported in part by the NSA grant H98230-06-1-0028.",

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T1 - Algebras associated to acyclic directed graphs

AU - Retakh, Vladimir

AU - Wilson, Robert Lee

N1 - Funding Information: States. E-mail addresses: vretakh@math.rutgers.edu (V. Retakh), rwilson@math.rutgers.edu (R.L. Wilson). 1 Both authors were supported in part by the NSA grant H98230-06-1-0028.

PY - 2009/1

Y1 - 2009/1

N2 - We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices and edges. Each finite acyclic directed graph admits countably many structures of a generalized layered graph. We construct linear bases in such algebras and compute their Hilbert series. Our interest to generalized layered graphs and algebras associated to those graphs is motivated by their relations to factorizations of polynomials over noncommutative rings.

AB - We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices and edges. Each finite acyclic directed graph admits countably many structures of a generalized layered graph. We construct linear bases in such algebras and compute their Hilbert series. Our interest to generalized layered graphs and algebras associated to those graphs is motivated by their relations to factorizations of polynomials over noncommutative rings.

KW - Factorizations of noncommutative polynomials

KW - Generalized layered graphs

KW - Hilbert series

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DO - 10.1016/j.aam.2008.04.002

M3 - Article

AN - SCOPUS:56449092543

SN - 0196-8858

VL - 42

SP - 42

EP - 59

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

IS - 1

ER -

Algebras associated to acyclic directed graphs

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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