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Let L=<L, v , ^ > and K=<K, v , ^ > be lattices, and let h:L->K. Then h is a lattice homomorphism if and only if for any a,b in L, h(a v b)=h(a) v h(b) and h(a ^ b)=h(a) ^ ...

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. A lattice isomorphism is a one-to-one and onto lattice homomorphism.

Lattice theory is the study of sets of objects known as lattices. It is an outgrowth of the study of Boolean algebras, and provides a framework for unifying the study of ...

A discrete subset of R^s which is closed under addition and subtraction and which contains Z^s as a subset.

Let L=(L, ^ , v ) and K=(K, ^ , v ) be lattices, and let h:L->K. A lattice endomorphism is a mapping h:L->L that preserves both meets and joins.

A lattice L is said to be oriented if there exists a rule which assigns a specified direction to any edge connecting arbitrary lattice points x_i,x_j in L. In that way, an ...

A distinct (including reflections and rotations) arrangement of adjacent squares on a grid, also called a fixed polyomino.

The root lattice of a semisimple Lie algebra is the discrete lattice generated by the Lie algebra roots in h^*, the dual vector space to the Cartan subalgebra.

A lattice graph, also known as a mesh graph or grid graph, is a graph possessing an embedding in a Euclidean space R^n that forms a regular tiling. Examples include grid ...

Let L=(L, ^ , v ) be a lattice, and let f,g:L->L. Then the pair (f,g) is a polarity of L if and only if f is a decreasing join-endomorphism and g is an increasing ...