Algebras associated to acyclic directed graphs

2007/07/24 by Vladimir Retakh, Retakh, Vladimir, Robert Lee Wilson +1 · 1 citation
Computer Science · Mathematics · #05E05 (Primary) #15A15 #16W30 (Secondary) #Advanced Algebra and Logic #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0707.3607

openalex publication_date 2007/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. Each finite directed acyclic 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.

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