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 (x₀, y₀)=(0, 0),(x₁, y₂),…,(x_n, y_n) , such that for all i, (x_i, y_i) and (x_i+1, y_i+1) 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 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.