**Counting All Self-Avoiding Walks on a Finite Lattice Strip of Width Two**

### Michael Nyblom,** RMIT **

Date: Friday 7th June

Time: 3:00pm–4:00pm (Talk & Q/A)

Venue: Building 8 Level 9 Room 66 (AGR) RMIT City campus

The seminar will be followed by snacks and drinks

All students, staff and visitors are welcome

**ABSTRACT:** In a two-dimensional square lattice a self-avoiding walk (SAW) is a path beginning at the origin which does not pass through the same lattice point twice. Specifically an *n* length SAW is a finite sequence of distinct lattice points (*x _{0}, y_{0}*)=(

*0, 0*),(

*x*),…,(

_{1}, y_{2}*x*) , such that for all

_{n}, y_{n}*i,*(

*x*) and (

_{i}, y_{i}*x*) are separated by a unit distance. The concept of a SAW is generally considered to have been introduced by the polymer chemist Orr around the mid-twentieth century. Despite their simplicity of definition, SAWs pose a number of open and perhaps intractable problems – in particular, the enumeration of all

_{i+1}, y_{i+1}*n*length SAWs on the square lattice, either by a closed-form expression or by some efficient algorithmic procedure. In this talk, I shall employ a combinatorial argument that does not require the use of generating functions

**BIOGRAPHY**: Michael Nyblom completed his doctoral studies in at RMIT in 1999. Michael enjoys teaching engineering mathematics and researching number theory.