Eric Babson

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We provide a polynomial time algorithm for computing the universal Gröbner basis of any polynomial ideal having a finite set of common zeros in fixed number of variables. One ingredient of our algorithm is an effective construction of the state polyhedron of any member of the Hilbert scheme Hilb d n of n-long d-variate ideals, enabled by introducing the(More)
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)
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)
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)
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