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

Authors: Margolis, Stuart and Saliola, Franco and Steinberg, Benjamin

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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