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The complex lattice Lambda_6^omega corresponding to real lattice K_(12) having the densest hypersphere packing (kissing number) in twelve dimensions. The associated ...

A lattice L is locally bounded if and only if each of its finitely generated sublattices is bounded. Every locally bounded lattice is locally subbounded, and every locally ...

For every positive integer n, there exists a circle which contains exactly n lattice points in its interior. H. Steinhaus proved that for every positive integer n, there ...

A lattice L is locally subbounded if and only if each of its finite subsets is contained in a finitely generated bounded sublattice of L. Every locally bounded lattice is ...

A generalization of the concept of set unions and intersections.

Perhaps the most commonly-studied oriented point lattice is the so-called north-east lattice which orients each edge of L in the direction of increasing coordinate-value. ...

The theta series of a lattice is the generating function for the number of vectors with norm n in the lattice. Theta series for a number of lattices are implemented in the ...

A lattice path from one point to another is p-good if it lies completely below the line y=(p-1)x. (1) Hilton and Pederson (1991) show that the number of p-good paths from (1, ...

As defined by Kyrmse, a canonical polygon is a closed polygon whose vertices lie on a point lattice and whose edges consist of vertical and horizontal steps of unit length or ...

A self-avoiding walk in which steps may be to the left, right, or straight ahead after a vertical step, but only straight ahead or to the left after a horizontal step. A ...