### Abstract

Original language | English |
---|---|

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 |

### Fingerprint

### Cite this

*Kyushu Journal of Mathematics*,

*67*(1), 117-127. https://doi.org/10.2206/kyushujm.67.117

**The incidence algebras of posets and acyclic categories.** / Quinn, David.

Research output: Contribution to journal › Article

*Kyushu Journal of Mathematics*, vol. 67, no. 1, pp. 117-127. https://doi.org/10.2206/kyushujm.67.117

}

TY - JOUR

T1 - The incidence algebras of posets and acyclic categories

AU - Quinn, David

PY - 2013/3

Y1 - 2013/3

N2 - 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.

AB - 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.

U2 - 10.2206/kyushujm.67.117

DO - 10.2206/kyushujm.67.117

M3 - Article

VL - 67

SP - 117

EP - 127

JO - Kyushu Journal of Mathematics

JF - Kyushu Journal of Mathematics

IS - 1

ER -