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2. Lattice (order) - Wikipedia

   en.wikipedia.org/wiki/Lattice_(order)

   A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).

3. Lattice model (physics) - Wikipedia

   en.wikipedia.org/wiki/Lattice_model_(physics)

   In mathematical physics, a lattice model is a mathematical model of a physical system that is defined on a lattice, as opposed to a continuum, such as the continuum of space or spacetime. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice.

4. Lattice (group) - Wikipedia

   en.wikipedia.org/wiki/Lattice_(group)

   A lattice in the sense of a 3-dimensional array of regularly spaced points coinciding with e.g. the atom or molecule positions in a crystal, or more generally, the orbit of a group action under translational symmetry, is a translation of the translation lattice: a coset, which need not contain the origin, and therefore need not be a lattice in ...

5. Complete lattice - Wikipedia

   en.wikipedia.org/wiki/Complete_lattice

   The standard definition from universal algebra states that a free complete lattice over a generating set is a complete lattice together with a function :, such that any function from to the underlying set of some complete lattice can be factored uniquely through a morphism from to .

6. Lattice path - Wikipedia

   en.wikipedia.org/wiki/Lattice_Path

   Lattice path of length 5 in ℤ 2 with S = { (2,0), (1,1), (0,-1) }.. In combinatorics, a lattice path L in the d-dimensional integer lattice ⁠ ⁠ of length k with steps in the set S, is a sequence of vectors ⁠,, …, ⁠ such that each consecutive difference lies in S. [1]

7. Hexagonal lattice - Wikipedia

   en.wikipedia.org/wiki/Hexagonal_lattice

   The honeycomb point set is a special case of the hexagonal lattice with a two-atom basis. [1] The centers of the hexagons of a honeycomb form a hexagonal lattice, and the honeycomb point set can be seen as the union of two offset hexagonal lattices. In nature, carbon atoms of the two-dimensional material graphene are arranged in a honeycomb ...

8. Ideal lattice - Wikipedia

   en.wikipedia.org/wiki/Ideal_lattice

   In general terms, ideal lattices are lattices corresponding to ideals in rings of the form [] / for some irreducible polynomial of degree . [1] All of the definitions of ideal lattices from prior work are instances of the following general notion: let be a ring whose additive group is isomorphic to (i.e., it is a free -module of rank), and let be an additive isomorphism mapping to some lattice ...

9. Lattice (discrete subgroup) - Wikipedia

   en.wikipedia.org/wiki/Lattice_(discrete_subgroup)

   Let be a locally compact group and a discrete subgroup (this means that there exists a neighbourhood of the identity element of such that = {}).Then is called a lattice in if in addition there exists a Borel measure on the quotient space / which is finite (i.e. (/) < +) and -invariant (meaning that for any and any open subset / the equality () = is satisfied).