Self-avoiding walks crossing a square and the gerrymander sequence.

by Prof. Tony Guttmann

Monday 17 Jun 2024, 15:00 → 16:30 Europe/Rome

1/1-2 - Aula "C. Voci" (Dipartimento di Fisica e Astronomia - Edificio Marzolo)

Self-avoiding walks crossing a square and the gerrymander sequence.

Tony Guttmann, School of Mathematics and Statistics, The University of Melbourne
 

We give an improved algorithm for the enumeration of self-avoiding walks and polygons within

an N x N square as well as for SAWs crossing a square. We present some proofs of the  asymptotic behaviour

as the size N of the square grows, and then show how one can numerically estimate the parameters in the asymptotic

expression. We then show how the improved algorithm can be adapted to count gerrymander sequences (OEIS A348456),

and prove that the asymptotics of the gerrymander sequence is similar to that of SAWs crossing a square.