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- Eric Babson, Shmuel Onn, Rekha Thomas
- 2002

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)

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)

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)

- Mohamed Omar, Jesús De Loera, Eric Babson, Brian Osserman
- 2011

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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