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...

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...

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...

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

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

citing Birkhoff, G. "Subdirect unions in universal algebra", Bull. Amer. Math. Soc. SO (1944), 764-768. See Birkhoff's representation theorem#The partial...

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...

geometry) Birkhoff–Von Neumann theorem (linear algebra) Birkhoff's representation theorem (lattice theory) Birkhoff's theorem (ergodic theory) Birkhoff's theorem...

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

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

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...

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...

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

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

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

In the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra...

(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...

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

{\displaystyle r>0} , are pre-compact. The Birkhoff–Kakutani theorem (named after mathematicians Garrett Birkhoff and Shizuo Kakutani) states that the following...

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...

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...

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

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

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

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...

In matrix theory, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive...

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