5 citations · 12 across the 6 of their papers we have counts for
12 papers
Computing the Ehrhart quasi-polynomial of a rational simplex
Alexander Barvinok
We present a polynomial time algorithm to compute any fixed number of the highest coefficients of the Ehrhart quasi-polynomial of a rational simplex. Previously such algorithms wer…
Low rank approximations of symmetric polynomials and asymptotic counting of contingency tables
Alexander Barvinok
We represent the number of mxn non-negative integer matrices (contingency tables) with prescribed row sums and column sums as the expected value of the permanent of a non-negative…
Integration and Optimization of Multivariate Polynomials by Restriction onto a Random Subspace
Alexander Barvinok
We consider the problem of efficient integration of an n-variate polynomial with respect to the Gaussian measure in R^n and related problems of complex integration and optimization…
Convex Geometry of Orbits
Alexander Barvinok, Grigoriy Blekherman
We study metric properties of convex bodies B and their polars B^o, where B is the convex hull of an orbit under the action of a compact group G. Examples include the Traveling Sal…
Random Weighting, Asymptotic Counting, and Inverse Isoperimetry
Alexander Barvinok, Alex Samorodnitsky
For a family X of k-subsets of the set 1,...,n, let |X| be the cardinality of X and let Gamma(X,mu) be the expected maximum weight of a subset from X when the weights of 1,...,n ar…
Short rational generating functions for lattice point problems
Alexander Barvinok, Kevin Woods
We prove that for any fixed d the generating function of the projection of the set of integer points in a rational d-dimensional polytope can be computed in polynomial time. As a c…