Lattices have some connections to the family of group-like algebraic structures. Because meet and join both commute and associate, a lattice can be viewed as consisting of two …

May 15, 2025 · Partial orders and lattices are important concepts in discrete mathematics and are widely used in computer science, especially in data structures, database theory, and the …

Aug 17, 2021 · In this section, we restrict our discussion to lattices, those posets for which every pair of elements has both a greatest lower bound and least upper bound. We first introduce …

Dec 3, 2025 · While every point lattice is a lattice under the ordering inherited from the plane, many lattices are not point lattices. Lattices offer a natural way to formalize and study the …

May 19, 2025 · What is a Lattice? Lattices, a fundamental concept in discrete mathematics and abstract algebra, serve as the backbone for numerous applications across computer science, …

Lecture 37: Intro to Lattices In this lecture, we will give a brief introduction to lattices, which are posets where any finite subset of elements has b. th an infimum and a supremum. We pro. …

May 6, 2025 · Lattices are like a grid in space made up of points. Imagine a huge sheet of graph paper spread out in multiple dimensions. Each point on this sheet is determined by a …

A lattice is defined as a partially ordered set (poset) in which any two elements have a unique meet (infimum) and a unique join (supremum). This structure satisfies specific conditions …

Zd is an integer lattice qZd is periodic modulo a small integer q. 0 Cryptographic functions based on q-ary lattices involve only arithmetic modulo q.

See Jacques Martinet's home page for a list of the known perfect lattices in 8 dimensions.