6 citations · 14 across the 6 of their papers we have counts for
6 papers
On (2,3)-agreeable Box Societies
Michael Abrahams, Meg Lippincott, Thierry Zell
The notion of -agreeable society was introduced by Deborah Berg et al.: a family of convex subsets of is called -agreeable if any subfamily of size contain…
Polynomial hierarchy, Betti numbers and a real analogue of Toda's theorem
Saugata Basu, Thierry Zell
Toda proved in 1989 that the (discrete) polynomial time hierarchy, , is contained in the class $\mathbf{P}^{#\mathbf{P}}$, namely the class of languages that can be de…
On Projections of Semi-algebraic Sets Defined by Few Quadratic Inequalities
Saugata Basu, Thierry Zell
Let be a compact semi-algebraic set defined by a system of polynomial inequalities of degree at most 2. π$ denote the standard projection from…
Topological complexity of the relative closure of a semi-Pfaffian couple
Thierry Zell
Gabrielov introduced the notion of relative closure of a Pfaffian couple as an alternative construction of the o-minimal structure generated by Khovanskii's Pfaffian functions. In…
Quantitative study of semi-Pfaffian sets
Thierry Zell
We study the topological complexity of sets defined using Khovanskii's Pfaffian functions, in terms of an appropriate notion of format for those sets. We consider semi- and sub-Pfa…
Topology of definable Hausdorff limits
Thierry Zell
Let be a set definable in an o-minimal expansion of the real field, be its projection, and assume that the non-empty fibers are…