Sal Barone

most citedOn a real analogue of Bezout inequality and the number of connected components of sign conditions

4 citations · 6 across the 2 of their papers we have counts for

collaborators

4 papers

math.AG2013★ 2 cited

Some Quantitative Results in Real Algebraic Geometry

Salvador Barone

Real algebraic geometry is the study of semi-algebraic sets, subsets of $R^{k}$ defined by Boolean combinations of polynomial equalities and inequalities. The focus of this thesis i…

math.AG2013★ 4 cited

On a real analogue of Bezout inequality and the number of connected components of sign conditions

Sal Barone, Saugata Basu

Let $R$ be a real closed field and $Q_{1}, \dots, Q_{ℓ} \in R [X_{1}, \dots, X_{k}]$ such that for each $i, 1 \leq i \leq ℓ$ , $deg (Q_{i}) \leq d_{i}$ . For $…

math.CO2011

Refined bounds on the number of connected components of sign conditions on a variety

Sal Barone, Saugata Basu

Let $R$ be a real closed field, $P, Q \subset R [X_{1}, ..., X_{k}]$ finite subsets of polynomials, with the degrees of the polynomials in $P$ (resp. $\math…

math.AG2011

On homotopy types of limits of semi-algebraic sets and additive complexity of polynomials

Sal Barone, Saugata Basu

We prove that the number of distinct homotopy types of limits of one-parameter semi-algebraic families of closed and bounded semi-algebraic sets is bounded singly exponentially in…