By combinatorial arguments, we prove that the number of self-avoiding walks on the strip {0, 1} × Z is 8Fn − 4 when n is odd and is 8Fn − n when n is even. Also, when backwards moves are prohibited, we derive simple expressions for the number of length n self-avoiding walks on {0, 1} × Z, Z× Z, the triangular lattice, and the cubic lattice.

Traits are fine-grained components that can be used to compose classes, while avoiding many of the problems of multiple inheritance and mixin-based approaches. Since most implementations of traits have focused on dynamically-typed languages, the question naturally arises, how can one best introduce traits to statically-typed languages, like Java and C#? In this paper we argue that the flattenin...

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 ...

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.

Abstract: We consider a long-range version of self-avoiding walk in dimension d > 2(α ∧ 2), where d denotes dimension and α the power-law decay exponent of the coupling function. Under appropriate scaling we prove convergence to Brownian motion for α ≥ 2, and to α-stable Lévy motion for α < 2. This complements results by Slade (1988), who proves convergence to Brownian motion for nearest-neighb...

The bond-true self-avoiding walk is a nearest neighbour random walk on Z, for which the probability of jumping along a bond of the lattice is proportional to exp(?g number of previous jumps along that bond). We prove a limit theorem for the distribution of the local time process of this walk. A consequence of the main theorem is a limit law for n ?3=2 T n where T n is the rst hitting time of th...

The self-avoiding walk, restricted to a strip, is considered in the context of linguistic combinatorics. AMS class!Jications: 05A15; 05E15; 60J15

In this paper, we propose a range-based localization algorithm to localize a wireless sensor network (WSN) in 2D. A widely used algorithm to localize a WSN in 2D is trilateration, which runs in polynomial time. Trilateration uses three distance measurements to localize a node. In some cases, the lack of connectivity leads to a low percentage of localized nodes since a node’s position can be fix...