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STACS
2004
Springer
13 years 10 months ago
Lattices with Many Cycles Are Dense
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...
Mårten Trolin
APPROX
2006
Springer
179views Algorithms» more  APPROX 2006»
13 years 9 months ago
On Bounded Distance Decoding for General Lattices
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...
Yi-Kai Liu, Vadim Lyubashevsky, Daniele Micciancio
COMBINATORICS
1998
60views more  COMBINATORICS 1998»
13 years 5 months ago
Finite Vector Spaces and Certain Lattices
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...
Thomas W. Cusick
DCG
1999
89views more  DCG 1999»
13 years 5 months ago
On Flag Vectors, the Dowling Lattice, and Braid Arrangements
Westudycomplexhyperplanearrangementswhoseintersectionlattices,known as the Dowling lattices, are a natural generalization of the partition lattice. We give a combinatorial descript...
Richard Ehrenborg, Margaret Readdy
COMBINATORICS
2000
97views more  COMBINATORICS 2000»
13 years 5 months ago
Counting Lattice Paths by Narayana Polynomials
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...
Robert A. Sulanke