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Combinatorial topology and the global dimension of algebras arising in combinatorics

Stuart MargolisFranco SaliolaBenjamin Steinberg — 2015

Journal of the European Mathematical Society

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...

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