Displaying similar documents to “Self-avoiding walks on the lattice ℤ² with the 8-neighbourhood system”

Classification systems and their lattice

Sándor Radeleczki (2002)

Discussiones Mathematicae - General Algebra and Applications

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We define and study classification systems in an arbitrary CJ-generated complete lattice L. Introducing a partial order among the classification systems of L, we obtain a complete lattice denoted by Cls(L). By using the elements of the classification systems, another lattice is also constructed: the box lattice B(L) of L. We show that B(L) is an atomistic complete lattice, moreover Cls(L)=Cls(B(L)). If B(L) is a pseudocomplemented lattice, then every classification system of L is independent...

Dual Lattice of ℤ-module Lattice

Yuichi Futa, Yasunari Shidama (2017)

Formalized Mathematics

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In this article, we formalize in Mizar [5] the definition of dual lattice and their properties. We formally prove that a set of all dual vectors in a rational lattice has the construction of a lattice. We show that a dual basis can be calculated by elements of an inverse of the Gram Matrix. We also formalize a summation of inner products and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL(Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic...

Random Walks in Attractive Potentials: The Case of Critical Drifts

Dmitry Ioffe, Yvan Velenik (2010)

Actes des rencontres du CIRM

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We consider random walks in attractive potentials - sub-additive functions of their local times. An application of a drift to such random walks leads to a phase transition: If the drift is small than the walk is still sub-ballistic, whereas the walk is ballistic if the drift is strong enough. The set of sub-critical drifts is convex with non-empty interior and can be described in terms of Lyapunov exponents (Sznitman, Zerner ). Recently it was shown that super-critical drifts lead to...

Incomparability with respect to the triangular order

Emel Aşıcı, Funda Karaçal (2016)

Kybernetika

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In this paper, we define the set of incomparable elements with respect to the triangular order for any t-norm on a bounded lattice. By means of the triangular order, an equivalence relation on the class of t-norms on a bounded lattice is defined and this equivalence is deeply investigated. Finally, we discuss some properties of this equivalence.

Residuation in orthomodular lattices

Ivan Chajda, Helmut Länger (2017)

Topological Algebra and its Applications

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We show that every idempotent weakly divisible residuated lattice satisfying the double negation law can be transformed into an orthomodular lattice. The converse holds if adjointness is replaced by conditional adjointness. Moreover, we show that every positive right residuated lattice satisfying the double negation law and two further simple identities can be converted into an orthomodular lattice. In this case, also the converse statement is true and the corresponence is nearly one-to-one. ...

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

Dangovski, Rumen (2012)

Serdica Mathematical Journal

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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.