# Bled'11 - 7th Slovenian International Conference on Graph Theory

19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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# The curious asymptotics of 3-sided prudent polygons

Presented by Prof. Anthony J GUTTMANN
Type: Oral presentation
Track: General session

## Content

In joint work with Nick Beaton (PhD student) and Philippe Flajolet, we have studied a range of solvable self-avoiding walk and polygon models. One of these, the so-called 3-sided prudent polygons, enumerated by area, displays quite unexpected asymptotics. Writing the dominant asymptotic form of the coefficients as $a_n \sim A \times \mu^n \times n^g,$ we find $g$ to be irrational, and more surprisingly, $A$ does not exist, due to the presence of long-period, small amplitude oscillatory component. We discuss this model and other models in this family.

## Place

Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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