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  1. Home > Articles & Issues >
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  3. Poset topology and h ...
Conference paper

Poset topology and homological invariants of algebras arising in algebraic combinatorics

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]
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Imported on
November 21, 2016
Published on
December 31, 2013
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Proceedings
DOI
10.46298/dmtcs.2381
License
https://about.hal.science/hal-authorisation-v1
Natural Sciences and Engineering Research Council of Canada
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706
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Poset topology and homological invariants of algebras arising in algebraic combinatorics

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]
Abstract
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.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • 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.
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Source: OpenCitations

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