## Combinatorics Seminar

When: Sunday, November 3, 10am
Where: Schreiber 309
Speaker: Alex Samorodnitsky, Hebrew University
Title: Bounds on the permanent of a doubly stochastic
matrix
## Abstract:

We show that the permanent of a doubly stochastic n-by-n matrix
A = (a_ij) is at least as large as
\prod_{i,j} (1-a_ij)^(1-a_ij)
and at most as large as 2^n times this number. Combined with
previous
work, this improves on the deterministic approximation factor for
the
permanent, giving 2^n instead of e^n-approximation.
If time allows, we will also discuss some more applications, such
as using the lower bound to prove S.Friedland's "Asymptotic Lower
Matching Conjecture" for the monomer-dimer problem.
Joint work with Leonid Gurvits.