On self-avoiding polygons and walks: the snake method via polygon joining
نویسندگان
چکیده
منابع مشابه
Compressed self-avoiding walks, bridges and polygons
We study various self-avoiding walks (SAWs) which are constrained to lie in the upper half-plane and are subjected to a compressive force. This force is applied to the vertex or vertices of the walk located at the maximum distance above the boundary of the half-space. In the case of bridges, this is the unique end-point. In the case of SAWs or self-avoiding polygons, this corresponds to all ver...
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We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40 we also calculate series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and the mean-square distance of a monome...
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This is the fourth installment of the five-part saga on the Umbral Transfer-Matrix method, based on Gian-Carlo Rota’s seminal notion of the umbra. In this article we describe the Maple packages USAP, USAW, and MAYLIS. USAP automatically constructs, for any specific r, an Umbral Scheme for enumerating, according to perimeter, the number of self-avoiding polygons with ≤ 2r horizontal edges per ve...
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We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40 we also calculate series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and the mean-square distance of a monome...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2019
ISSN: 1083-6489
DOI: 10.1214/18-ejp249