Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
Title: Power series expansion of the free energy for monomer-dimer tilings.
Speaker: Gleb Pogudin, New York University
Date: Thursday, February 1, 2018 5:00pm
Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ
Let a(n, p), where 0 < p < 1, be the number of tilings of n-by-n square with dimers and monomers, such that dimers occupy approximately p of the area. Then the following limit characterizes the growth of this number and is called the free energy of the monomer-dimer system:
It is an open problem how to compute f(p). I will describe a method allowing to compute the first 63 terms of its Taylor expansion at zero. This yields to accurate estimates for many values of p. I will also discuss other approaches to computing f(p) and interesting mathematical problems connected with them.