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On self-avoiding walks on certain grids and the connective constant

Dangovski, Rumen — 2012

Serdica Mathematical Journal

2010 Mathematics Subject Classification: Primary: 05C81. Secondary: 60G50. We consider self-avoiding walks on the square grid graph. More precisely we investigate the number of walks of a fixed length on Z×{-1,0,1}. Using combinatorial arguments we derive the related generating function. We present the asymptotic estimates of the number of walks in consideration, as well as important connective constants.

Self-Avoiding Walks in the Plane Несамопресичащи се разходки в равнината

Dangovski, RumenPetrova, Kalina — 2012

Union of Bulgarian Mathematicians

Румен Руменов Данговски, Калина Христова Петрова - Разглеждаме броя на несамопресичащите се разходки с фиксирана дължина върху целочислената решетка. Завършваме анализа върху случая за лента, с дължина едно. Чрез комбинаторни аргументи получаваме точна формула за броя на разходките върху лента, ограничена отляво и отдясно. Формулата я изследваме и асимптотично. We examine the number of self-avoiding walks with a fixed length on the square grid graph and more specifically we complete...

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