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Motivated by the Coxeter complex associated to a Coxeter system (W, S), we introduce a simplicial regular cell complex ∆(G, S) with a G-action associated to any pair (G, S) where G is a group and S is a finite set of generators for G which is minimal with respect to inclusion. We examine the topology of ∆(G, S), and in particular the representations of G on… (More)

Certain necessary conditions on the face numbers and Betti numbers of sim-plicial complexes endowed with a proper action of a prime order cyclic group are established. A notion of colored algebraic shifting is defined and its properties are studied. As an application a new simple proof of the characterization of the flag face numbers of balanced… (More)

We define a set of invariants of a homogeneous ideal I in a polynomial ring called the symmetric iterated Betti numbers of I. For I Γ , the Stanley-Reisner ideal of a simplicial complex Γ, these numbers are the symmetric counterparts of the exterior iterated Betti numbers of Γ introduced by Duval and Rose. We show that the symmetric iterated Betti numbers… (More)

A permutation σ describing the relative orders of the first n iterates of a point x under a self-map f of the interval I = [0, 1] is called an order pattern. For fixed f and n, measuring the points x ∈ I (according to Lebesgue measure) that generate the order pattern σ gives a probability distribution µ n (f) on the set of length n permutations. We study… (More)

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