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A lattice-ordered set is a poset (L,<=) in which each two-element subset {a,b} has an infimum, denoted inf{a,b}, and a supremum, denoted sup{a,b}. There is a natural ...

The Barnes-Wall lattice is a d-dimensional lattice that exists when d is a power of 2. It is implemented in the Wolfram Language as LatticeData[{"BarnesWall", n}]. Special ...

A uniquely complemented lattice is a complemented lattice (L, ^ , v ,0,1,^') that satisfies ( forall x in L)( forall y in L)[(x ^ y=0) ^ (x v y=1)]=>y=x^'. The class of ...

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. ...

Let L be a finite-dimensional split semisimple Lie algebra over a field of field characteristic 0, H a splitting Cartan subalgebra, and Lambda a weight of H in a ...