In this paper, we prove reconstruction results for truncated lattices. The main results are that truncated lattices that contain a 4-crown and truncated semi-modular lattices are reconstructible. Reconstruction of the truncated lattices not covered by this work appears challenging. Indeed, the remai
Genomorphisms of semi-modular lattices
β Scribed by Damas P. Gruska
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 361 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0022-0000
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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]
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
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.
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