On Walks Avoiding a Quadrant
نویسندگان
چکیده
منابع مشابه
Square lattice walks avoiding a quadrant
In the past decade, a lot of attention has been devoted to the enumeration of walks with prescribed steps confined to a convex cone. In two dimensions, this means counting walks in the first quadrant of the plane (possibly after a linear transformation). But what about walks in non-convex cones? We investigate the two most natural cases: first, square lattice walks avoiding the negative quadran...
متن کاملSelf-avoiding walks, neighbour-avoiding walks and trails on semiregular lattices
We study self-avoiding and neighbour-avoiding walks and lattice trails on two semiregular lattices, the (3.122) lattice and the (4.82) lattice. For the (3.122) lattice we find the exact connective constant for both self-avoiding walks, neighbour-avoiding walks and trails. For the (4.82) lattice we generate long series which permit the accurate estimation of the connective constant for self-avoi...
متن کاملAnisotropic Self - Avoiding Walks
We consider a model of self-avoiding walks on the lattice Zd with different weights for steps in each of the 2d lattice directions. We find that the directiondependent mass for the two-point function of this model has three phases: mass positive in all directions; mass identically −∞; and masses of different signs in different directions. The final possibility can only occur if the weights are ...
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 کاملExtendable Self-avoiding Walks
The connective constant μ of a graph is the exponential growth rate of the number of n-step self-avoiding walks starting at a given vertex. A self-avoiding walk is said to be forward (respectively, backward) extendable if it may be extended forwards (respectively, backwards) to a singly infinite self-avoiding walk. It is called doubly extendable if it may be extended in both directions simultan...
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: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/8019