Let P be a convex polytope containing the origin, whose dual is a lattice polytope. Hibi’s Palindromic Theorem tells us that if P is also a lattice polytope then the Ehrhart δ-vector of P is palindromic. Perhaps less well-known is that a similar result holds when P is rational. We present an elementary lattice-point proof of this fact.

Matching 2-lattice polyhedra are a special class of lattice polyhedra that include network 3ow polyhedra, fractional matching polyhedra, matroid intersection polyhedra, etc. In this paper we develop a polynomial-time extreme point algorithm for #nding a maximum cardinality vector in a matching 2-lattice polyhedron. c © 2001 Elsevier Science B.V. All rights reserved.

To an integral lattice L in the euclidean space (R, (, )), one associates the set of characteristic vectors v ∈ R with (v, x) ≡ (x, x) mod 2Z for all x ∈ L. They form a coset modulo 2L, where L = {v ∈ R | (v, x) ∈ Z ∀x ∈ L} is the dual lattice of L. Recall that L is called integral, if L ⊂ L and unimodular, if L = L. For a unimodular lattice, the square length of a characteristic vector is cong...

A central problem in the algorithmic study of lattices is the closest vector problem: given a lattice L represented by some basis, and a target point y, nd the lattice point closest to y. Bounded Distance Decoding is a variant of this problem in which the target is guaranteed to be close to the lattice, relative to the minimum distance 1(L) of the lattice. Speci cally, in the -Bounded Distance ...

1.2. Let E be a Euclidean vector space, Φ ⊂ E∗ a root system. Denote Q ⊂ h∗ the root lattice, and P ⊂ h∗ the weight lattice. Let Q∨ ⊂ E be the lattice generated by the coroots α∨, α ∈ Φ, the coroot lattice is dual to the weight lattice P ⊂ h∗, and P∨ ⊂ E the dual weight lattice, which is dual to the root lattice Q. Let H = HomZ(P,C) = Q∨ ⊗Z C∗ be the complex algebraic torus with Lie algebra h =...

Lattice basis reduction is the problem of finding short vectors in lattices. The security of lattice based cryptosystems is based on the hardness of lattice reduction. Furthermore, lattice reduction is used to attack well-known cryptosystems like RSA. One of the algorithms used in lattice reduction is the enumeration algorithm (ENUM), that provably finds a shortest vector of a lattice. We prese...

We consider the design of lattice vector quantizers for the problem of coding Gaussian sources with uncoded side information available only at the decoder. The design of such quantizers can be reduced to the problem of nding an appropriate sublattice of a given lattice codebook. We study the performance of the resulting quantizers in the limit as the encoding rate becomes high, and we evaluate ...

We present a quenched lattice calculation of the weak nucleon form factors: vector (FV (q )), induced tensor (FT (q )), axial-vector (FA(q )) and induced pseudo-scalar (FP (q )) form factors. Our simulations are performed on three different lattice sizes L × T = 24 × 32, 16 × 32 and 12 × 32 with a lattice cutoff of a ≈ 1.3 GeV and light quark masses down to about 1/4 the strange quark mass (mπ ...

On Operators whose Compactness Properties are defined by Order by Safak Alpay Abstract. Let E be a Banach lattice. A subset B of E is called order bounded if there exist a, b in E such that a ≤ x ≤ b for each x ∈ B. Considering E in E′′, the bidual of E, a subset B of E is called b-order bounded in E if it is order bounded in the Banach lattice E′′. A bounded linear operator T : E → X is called...