Poset topology and homological invariants of algebras arising in algebraic combinatorics

Stuart Margolis; Franco Saliola; Benjamin Steinberg

doi:10.46298/dmtcs.2381

Stuart Margolis ; Franco Saliola ; Benjamin Steinberg - Poset topology and homological invariants of algebras arising in algebraic combinatorics

dmtcs:2381 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) - https://doi.org/10.46298/dmtcs.2381

Poset topology and homological invariants of algebras arising in algebraic combinatorics

Authors: Stuart Margolis ¹; Franco Saliola ²; Benjamin Steinberg ³

1 Department of Mathematics [Bar-Ilan]
2 Laboratoire de combinatoire et d'informatique mathématique [Montréal]
3 City College of New York [CUNY]

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.

https://doi.org/10.46298/dmtcs.2381

Source: 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

Imported 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]

Funding:

Source : OpenAIRE Graph

Funder: Natural Sciences and Engineering Research Council of Canada

Linked publications - datasets - softwares

Source : ScholeXplorer IsRelatedTo ARXIV math/0601745 Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.jcta.2006.01.005 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.math/0601745 10.48550/arxiv.math/0601745 10.1016/j.jcta.2006.01.005 math/0601745 Intersections of Leray complexes and regularity of monomial ideals

Stuart Margolis ; Franco Saliola ; Benjamin Steinberg - Poset topology and homological invariants of algebras arising in algebraic combinatorics

Linked publications - datasets - softwares

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