Speaker:

Thomas Prellberg (QMUL)

Date/Time:

Mon, 08/10/2012 - 17:30

Room:

M103

Seminar series:

Recently Alan Sokal studied the leading root $x_0(q)$ of the partial theta function

$\Theta_0(x,q)=\sum\limits_{n=0}^\infty x^nq^{\binom n2}$, considered as a formal

power series. He proved that all the coefficients of

$-x_0(q)=1+q+2q^2+4q^3+9q^4+\ldots$

are positive integers.

In this talk I will present an explicit combinatorial interpretation of these coefficients.

More precisely, I will show that $-x_0(q)$ enumerates rooted trees that are enriched by

certain polyominoes, weighted according to their total area.