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Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometry. (arXiv:1508.05446v2 [math.CO] UPDATED)
来源于:arXiv
In recent years it has been noted that a number of combinatorial structures
such as real and complex hyperplane arrangements, interval greedoids, matroids
and oriented matroids have the structure of a finite monoid called a left
regular band. Random walks on the monoid model a number of interesting Markov
chains such as the Tsetlin library and riffle shuffle. The representation
theory of left regular bands then comes into play and has had a major influence
on both the combinatorics and the probability theory associated to such
structures. In a recent paper, the authors established a close connection
between algebraic and combinatorial invariants of a left regular band by
showing that certain homological invariants of the algebra of a left regular
band coincide with the cohomology of order complexes of posets naturally
associated to the left regular band.
The purpose of the present monograph is to further develop and deepen the
connection between left regular bands and poset topology. T 查看全文>>