Results 1 to 10 of about 70,685 (147)
Congruence for Lattice Path Models with Filter Restrictions and Long Steps [PDF]
Mathematics, 2022 We derive a path counting formula for a two-dimensional lattice path model with filter restrictions in the presence of long steps, source and target points of which are situated near the filters. This solves the problem of finding an explicit formula for
Dmitry Solovyev
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On the Uniqueness of Lattice Characterization of Groups
Axioms, 2023 We analyze the problem of the uniqueness of characterization of groups by their weak congruence lattices. We discuss the possibility that the same algebraic lattice L acts as a weak congruence lattice of a group in more than one way, so that the ...
Jelena Jovanović +2 more
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A solution to Dilworth's congruence lattice problem [PDF]
Advances in Mathematics, 2007 Version 1 presents a longer and slightly more general proof, based on so-called "uniform refinement properties". Version 2 presents a shorter proof. Versions 3 an 4 add a few minor improvements.
F. Wehrung
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A uniform refinement property for congruence lattices [PDF]
, 2005 The Congruence Lattice Problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of a lattice. It was hoped that a positive solution would follow from E. T. Schmidt's construction or from the approach of P. Pudlak,
Wehrung, Friedrich
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International Journal of Multidisciplinary in Cryptology and Information Security, 2023 Many digital signature schemes have been proposed based on different mathematical problems. Some of them are based on factoring into primes, discrete logarithm problem, elliptic curve discrete logarithm problem, lattice problem, multivariate quadratic ...
semanticscholar +1 more source
Unsolvable one-dimensional lifting problems for congruence lattices of lattices [PDF]
Forum Mathematicum, 2002 Let S be a distributive { , 0}-semilattice. In a previous paper, the second author proved the following result: Suppose that S is a lattice. Let K be a lattice, let $ $: Con K $\to$ S be a { , 0}-homomorphism. Then $ $ is, up to isomorphism, of the form Conc f, for a lattice L and a lattice homomorphism f : K $\to$ L. In the statement above, Conc
Tuma, Jiri, Wehrung, Friedrich
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The congruence kernel of an arithmetic lattice in a rank one algebraic group over a local field [PDF]
, 2007 Let k be a global field and let kυ be the completion of k with respect to υ a non-archimedean place of k. Let G be a connected, simply-connected algebraic group over k, which is absolutely almost simple of kυ -rank 1. Let G = G(kυ ).
A. Mason +3 more
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Representation growth and representation zeta functions of groups [PDF]
, 2012 We give a short introduction to the subject of representation growth and representation zeta functions of groups, omitting all proofs. Our focus is on results which are relevant to the study of arithmetic groups in semisimple algebraic groups, such as ...
Klopsch, Benjamin
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Congruences and Trajectories in Planar Semimodular Lattices
Discussiones Mathematicae - General Algebra and Applications, 2018 A 1955 result of J. Jakubík states that for the prime intervals p and q of a finite lattice, con(p) ≥ con(q) iff p is congruence-projective to q (via intervals of arbitrary size).
Grätzer G.
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An open problem on congruences of finite lattices
, 2023 Let $L$ be a planar semimodular lattice. We call $L$ \emph{slim}, if it has no $\mthree$ sublattice. Let us define an \emph{SPS lattice} as a slim, planar, semimodular lattice $L$. In 2016, I proved a property of congruences of SPS lattices (Two-cover Property) and raised the problem of characterizing them.
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