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- Steven R Finch
- 1998

This is a brief survey of certain constants associated with random lattice models, including self-avoiding walks, polyominoes, the Lenz-Ising model, monomers and dimers, ice models, hard squares and hexagons, and percolation models. 1. Introduction Random lattice models give rise to combinatorial problems that are often easily-stated but intractable. This… (More)

k) , t h e n t h e o p t i m a l s t r a t e g y i s t o r e j e c t t h e fi r s t m − 1 a p p l i c a n t s a n d a c c e p t t h e n e x t c a n d i d a t e , w h e r 1 ] c a l c u l a t e d t h e a s y m p t o t i c p r o b a b i l i t y o f s u c c e s s t o b e [ 1 2 ,

- Steven R Finch
- 2005

When searching for a planar line, if given no further information , one should adopt a logarithmic spiral strategy (although unproven). This brief paper is concerned entirely with geometry in the plane and continues a thought in [1]. If a line intersects a circle in one or two points, we say that the line strikes the circle. If a line intersects a circle in… (More)

- Steven R Finch
- 2014

Given a positive integer n, let P(n) denote the largest prime factor of n and S(n) denote the smallest integer m such that n divides m! The function S(n) is known as the Smarandache function and has been intensively studied [1]. Its behavior is quite erratic [2] and thus all we can reasonably hope for is a statistical approximation of its growth, e.g., an… (More)