The incidence algebras of posets and acyclic categories

David Quinn

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1 Citation (Scopus)


Acyclic categories were introduced by Kozlov and can be viewed as generalized posets. Similar to posets, one can define their incidence algebras and a related topological complex. We consider the incidence algebra of either a poset or acyclic category as the quotient of a path algebra by the parallel ideal. We show that this ideal has a quadratic Gröbner basis with a lexicographic monomial order if and only if the poset or acyclic category is lexshellable.
Original languageEnglish
Pages (from-to)117-127
Number of pages11
JournalKyushu Journal of Mathematics
Issue number1
Publication statusPublished - Mar 2013


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