Abstract
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 language | English |
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Pages (from-to) | 117-127 |
Number of pages | 11 |
Journal | Kyushu Journal of Mathematics |
Volume | 67 |
Issue number | 1 |
DOIs | |
Publication status | Published - Mar 2013 |