Abstract We give a method for approximating any n-dimensional lattice with a lattice Λ whose factor group Zn /Λ has n − 1 cycles of equal length with arbitrary precision. We al...
A central problem in the algorithmic study of lattices is the closest vector problem: given a lattice v represented by some basis, and a target point y, nd the lattice point close...
The Galois number Gn(q) is defined to be the number of subspaces of the n-dimensional vector space over the finite field GF(q). When q is prime, we prove that Gn(q) is equal to...
Westudycomplexhyperplanearrangementswhoseintersectionlattices,known as the Dowling lattices, are a natural generalization of the partition lattice. We give a combinatorial descript...
Let d(n) count the lattice paths from (0, 0) to (n, n) using the steps (0,1), (1,0), and (1,1). Let e(n) count the lattice paths from (0, 0) to (n, n) with permitted steps from th...