Lattice-point enumerators of ellipsoids

Dedekind–Carlitz Polynomials as Lattice-Point Enumerators in Rational Polyhedra

We study higher-dimensional analogs of the Dedekind–Carlitz polynomials c (u, v; a, b) := b−1 X

COMPUTATIONAL ENUMERATION OF POINT DEFECT CLUSTERS IN DOUBLE- LATTICE CRYSTALS

The cluster representation matrices have already been successfully used to enumerate close-packed vacancy clusters in all single-lattice crystals [I, 2]. Point defect clusters in double-lattice crystals may have identical geometry but are distinct due to unique atomic postions enclosing them. The method of representation matrices is extended to make it applicable to represent and enumerate ...

Lattice point simplices

We consider simplices in [w” with lattice point vertices, no other boundary lattice points and n interior lattice points, with an emphasis on the barycentric coordinates of the interior points. We completely classify such triangles under unimodular equivalence and enumerate. For example, in a lattice point triangle with exactly one interior point, that point must be the centroid. We discuss the...

Representations of lattice point sets

Quantum shadow enumerators

In a recent paper [7], Shor and Laflamme define two “weight enumerators” for quantum error correcting codes, connected by a MacWilliams transform, and use them to give a linear-programming bound for quantum codes. We extend their work by introducing another enumerator, based on the classical theory of shadow codes, that tightens their bounds significantly. In particular, nearly all of the codes...