We present a beautiful interplay between combinatorial topology and homological algebra for a class of monoids that arise naturally in algebraic combinatorics. We explore several applications of this interplay. For instance, we provide a new interpretation of the Leray number of a clique complex in terms of non-commutative algebra.

Source : oai:HAL:hal-01207594v1

Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)

Section: Proceedings

Published on: January 1, 2014

Submitted on: November 21, 2016

Keywords: left regular band,hyperplane arrangement,order complex,cohomology,poset topology,CW poset,Leray number,chordal graph,global dimension,hereditary algebra,(minimal) projective resolutions,Koszul algebra.,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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