In
mathematics, a
self-avoiding walk (
SAW) is a
sequence of moves on a
lattice (a
lattice path) that does not visit the same point more than once. This is a special case of the
graph theoretical notion of a
path. A
self-avoiding polygon (
SAP) is a closed self-avoiding walk on a lattice. SAWs were first introduced by the chemist
Paul Flory in order to model the real-life behavior of chain-like entities such as
solvents and
polymers, whose physical volume prohibits multiple occupation of the same spatial point. Very little is known rigorously about the self-avoiding walk from a mathematical perspective, although physicists have provided numerous conjectures that are believed to be true and are strongly supported by numerical simulations.