منابع مشابه
Prudent walks and polygons
We have produced extended series for two-dimensional prudent polygons, based on a transfer matrix algorithm of complexity O(n), for a series of length n. We have extended the definition to three dimensions and produced series expansions for both prudent walks and polygons in three dimensions. For prudent polygons in two dimensions we find the growth constant to be smaller than that for the corr...
متن کاملPrudent Self-Avoiding Walks
We have produced extended series for prudent self-avoiding walks on the square lattice. These are subsets of self-avoiding walks. We conjecture the exact growth constant and critical exponent for the walks, and show that the (anisotropic) generating function is almost certainly not differentiably-finite.
متن کاملFamilies of prudent self-avoiding walks
A self-avoiding walk (SAW) on the square lattice is prudent if it never takes a step towards a vertex it has already visited. Prudent walks differ from most classes of SAW that have been counted so far in that they can wind around their starting point. Their enumeration was first addressed by Préa in 1997. He defined 4 classes of prudent walks, of increasing generality, and wrote a system of re...
متن کاملWalks on Borders of Polygons
We give a graph theoretical proof for the existence of a walk connecting left and right sides of a rectangle when it is partitioned into (finitely many) rectangles colored in a specific way, and the walk is aloud to use only borders between rectangles of different color. The problem was originally introduced by J.R. Isbell in the proof of his Zig-Zag Theorem. We prove the existence of such a wa...
متن کاملCompressed self-avoiding walks, bridges and polygons
We study various self-avoiding walks (SAWs) which are constrained to lie in the upper half-plane and are subjected to a compressive force. This force is applied to the vertex or vertices of the walk located at the maximum distance above the boundary of the half-space. In the case of bridges, this is the unique end-point. In the case of SAWs or self-avoiding polygons, this corresponds to all ver...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2009
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/42/9/095205