Geodesic
Combinatorial topology and the global dimension of algebras arising in combinatorics
Journal of the European Mathematical Society, Tome 17 (2015) no. 12, pp. 3037-3080 Cet article a éte moissonné depuis la source EMS Press

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In a highly influential paper, Bidigare, Hanlon and Rockmore showed that a number of popular Markov chains are random walks on the faces of a hyperplane arrangement. Their analysis of these Markov chains took advantage of the monoid structure on the set of faces. This theory was later extended by Brown to a larger class of monoids called left regular bands. In both cases, the representation theory of these monoids played a prominent role. In particular, it was used to compute the spectrum of the transition operators of the Markov chains and to prove diagonalizability of the transition operators.
DOI : 10.4171/jems/579
Classification : 05-XX, 13-XX
Keywords: Global dimension, hereditary algebra, cohomology, classifying space, left regular band, hyperplane arrangements, order complex, Leray number, chordal graph 
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     title = {Combinatorial topology and the global dimension of algebras arising in combinatorics},
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     year = {2015},
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Stuart Margolis; Franco Saliola; Benjamin Steinberg. Combinatorial topology and the global dimension of algebras arising in combinatorics. Journal of the European Mathematical Society, Tome 17 (2015) no. 12, pp. 3037-3080. doi: 10.4171/jems/579

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