Combinatorial problems with stretched exponential asymptotics
Seminar/Forum
Evan WIlliams Theatre
Peter Hall Building
We look at a range of combinatorial problems where the growth of coefficients is of the form $C.\mu^n\cdot \exp(\alpha n^{\beta}) \cdot n^g,$ with $\alpha > 0,$ $0 < \beta < 1.$ Problems include some patternavoiding permutations, pushed" random walks,
pushed" selfavoiding walks and interacting partiallydirected walks. We will discuss, in a handwaving way, how this stretchedexponential term arises, and give a numerical method for estimating the parameters $\mu,$ $\alpha,$ $\beta$ and $g.$ This new method arises from some recent investigations in number theory with Richard Brent and Larry Glasser. As an example, we give more precise asymptotics for the coefficients of $Av(1324)$ patternavoiding permutations.
Presenter

Professor Tony Guttmann, The University of Melbourne