Hamiltonian and exclusion statistics approach to discrete forward-moving paths

Kinetic Approach to Fractional Exclusion Statistics

Abstract: We show that the kinetic approach to statistical mechanics permits an elegant and efficient treatment of fractional exclusion statistics. By using the exclusion-inclusion principle recently proposed [Phys. Rev. E 49, 5103 (1994)] as a generalization of the Pauli exclusion principle, which is based on a proper definition of the transition probability between two states, we derive a var...

On Hamiltonian cycles and Hamiltonian paths

A Hamiltonian cycle is a spanning cycle in a graph, i.e., a cycle through every vertex, and a Hamiltonian path is a spanning path. In this paper we present two theorems stating sufficient conditions for a graph to possess Hamiltonian cycles and Hamiltonian paths. The significance of the theorems is discussed, and it is shown that the famous Ore’s theorem directly follows from our result.  2004...

An Approach to Deriving Maximal Invariant Statistics

Invariance principles is one of the ways to summarize sample information and by these principles invariance or equivariance decision rules are used. In this paper, first, the methods for finding the maximal invariant function are introduced. As a new method, maximal invariant statistics are constructed using equivariant functions. Then, using several equivariant functions, the maximal invariant...

Defining Integrated Knowledge Translation and Moving Forward: A Response to Recent Commentaries

Hamiltonian Paths and Hyperbolic Patterns

In 1978 I thought it would be possible to design a computer algorithm to draw repeating hyperbolic patterns in a Poincaré disk based on Hamiltonian paths in their symmetry groups. The resulting successful program was capable of reproducing each of M.C. Escher’s four “Circle Limit” patterns. The program could draw a few other patterns too, but was somewhat limited. Over the years I have collabor...