Algebras associated to acyclic directed graphs

Vladimir Retakh, Robert Lee Wilson

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 languageEnglish (US)
Pages (from-to)42-59
Number of pages18
JournalAdvances in Applied Mathematics
Issue number1
StatePublished - Jan 2009

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


  • Factorizations of noncommutative polynomials
  • Generalized layered graphs
  • Hilbert series


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