other similarly named results, see Birkhoff's theorem (disambiguation). In mathematics, Birkhoff's representation theorem for distributive lattices states...

Birkhoff's theorem may refer to several theorems named for the American mathematician George David Birkhoff: Birkhoff's theorem (relativity) Birkhoff's...

is Cayley's original theorem. Wagner–Preston theorem is the analogue for inverse semigroups. Birkhoff's representation theorem, a similar result in order...

over time. A generalization of Birkhoff's theorem is Kingman's subadditive ergodic theorem. Birkhoff–Khinchin theorem. Let ƒ be measurable, E(|ƒ|) < ∞...

algebra of endomorphisms of some finite-dimensional vector space. Birkhoff's HSP theorem states that every model of an algebra A is the homomorphic image...

non-negative and less than or equal to 1. The Birkhoff–von Neumann theorem (often known simply as Birkhoff's theorem) states that the polytope B n {\displaystyle...

Zeilberger–Bressoud theorem (combinatorics) Birkhoff's representation theorem (lattice theory) Boolean prime ideal theorem (mathematical logic) Bourbaki–Witt theorem (order...

Birkhoff's representation theorem Birkhoff's HSP theorem Birkhoff's theorem Birkhoff–Kakutani theorem Pierce–Birkhoff conjecture Pierce–Birkhoff ring...

bounded distributive lattices. Representation theorem Birkhoff's representation theorem Stone's representation theorem for Boolean algebras Stone duality...

ones that hold in all lattices of sets in the above sense. Birkhoff's representation theorem for distributive lattices states that every finite distributive...

graph of a distributive lattice that may be obtained via Birkhoff's representation theorem from a zigzag poset, a partially ordered set defined by an...

specifically in the theory of Lie algebras, the Poincaré–Birkhoff–Witt theorem (or PBW theorem) is a result giving an explicit description of the universal...

distributive lattice generated by X . {\displaystyle X.} Birkhoff's representation theorem for distributive lattices states that every finite distributive...

In mathematics, the Birkhoff–Grothendieck theorem classifies holomorphic vector bundles over the complex projective line. In particular every holomorphic...

vertices, that every finite partial order is equivalent by Birkhoff's representation theorem to a finite distributive lattice, it follows that every finite...

to x. The result is a distributive lattice and is used in Birkhoff's representation theorem. However, it may have many more elements than are needed to...

exists a representation of the desired form. Atiyah–Bott fixed-point theorem Banach fixed-point theorem Bekić's theorem Borel fixed-point theorem Bourbaki–Witt...

is isomorphic to a lattice of sets, ordered by inclusion (Birkhoff's representation theorem). A semilattice is partially ordered set with only one of...

described in the 1970s by John Horton Conway and Donald Knuth. By Birkhoff's representation theorem, this lattice can be represented as the lower sets of an underlying...

lattice with this many elements, generated from a fence via Birkhoff's representation theorem, has as its graph the Fibonacci cube. A partially ordered...

sets; in the case of finite distributive lattices, this is Birkhoff's representation theorem and the sets may be taken as the lower sets of a partially...

(with continuous mappings). Another case of Stone duality is Birkhoff's representation theorem stating a duality between finite partial orders and finite...

Stone duality, connecting sober spaces and spatial locales. Birkhoff's representation theorem relating distributive lattices and partial orders Pontryagin...

and to make clear the ramifications of the parallel postulate. Birkhoff's axioms: Birkhoff proposed four postulates for Euclidean geometry that can be confirmed...

class of partial orders, called distributive lattices; see Birkhoff's representation theorem. Sequence A001035 in OEIS gives the number of partial orders...

antimatroid forming the linear extensions of the partial order. By Birkhoff's representation theorem for distributive lattices, the feasible sets in a poset antimatroid...

operations, forms a distributive lattice, the lattice given by Birkhoff's representation theorem from the partially ordered set of subsets of the n {\displaystyle...

and finite topologies can be interpreted as a version of Birkhoff's representation theorem, an equivalence between finite distributive lattices (the...

the theorem that every finite Boolean lattice is isomorphic to the lattice of subsets of a finite set, and (less trivially) Birkhoff's representation theorem...

and set intersection. The name "quasi-ordinal" arises from Birkhoff's representation theorem, which explains that distributive lattices uniquely correspond...