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Matching in modular lattices

✍ Scribed by Dwight Duffus

Publisher: Elsevier Science
Year: 1982
Tongue: English
Weight: 542 KB
Volume: 32
Category: Article
ISSN: 0097-3165
DOI: 10.1016/0097-3165(82)90047-4

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📜 SIMILAR VOLUMES

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✍ Klaus Reuter 📂 Article 📅 1987 🏛 Elsevier Science 🌐 English ⚖ 181 KB

Given a finite lattice L, let J(L) (M(L)) denote the set of nonzero join irreducible (nonunit meet irreducible) elements of L. A finite lattice L is said to be linearly indecomposable if there do not exist x, y E L with x < y such that z cx or z 2 y for all z E L\{x, y}. We prove: Every finite linea

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Even lattices similar to their duals are discussed in connection with modular forms for Fricke groups. In particular, lattices of level 2 with large Hermite number are considered, and an analogy between the seven levels \(l\) such that \(1+l\) divides 24 is stressed. "t 1995 Academic Press, Inc.

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✍ Gabriele Nebe; Boris B. Venkov 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 353 KB

In this note we consider integral lattices 4 in euclidean space (R n , ,), i.e. 4 R n is the Z-span of an R-basis of R n with ,(4, 4) Z. The minimum of 4 is min[,(4, 4) | 0{\* # 4]. It is interesting to find lattices of given determinant or of given genus with large minimum. We prove the following

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Left-modularity is a concept that generalizes the notion of modularity in lattice theory. In this paper, we give a characterization of left-modular elements and derive two formulae for the characteristic polynomial, /, of a lattice with such an element, one of which generalizes Stanley's theorem [6]

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We show that in the case of 2-dimensional lattices, Quebbemann's notion of modular and strongly modular lattices has a natural extension to the class group of a given discriminant, in terms of a certain set of translations. In particular, a 2-dimensional lattice has ``extra'' modularities essentiall

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