In mathematics, in the areas of order theory and combinatorics, Dilworth's theorem states that, in any finite partially ordered set, the maximum size of...

orders the two theorems differ, and (as Mirsky observes) Dilworth's theorem is more difficult to prove. Mirsky's theorem and Dilworth's theorem are also related...

the proofs uses Dilworth's theorem on chain decompositions in partial orders, or its simpler dual (Mirsky's theorem). To prove the theorem, define a partial...

Philadelphia, Pennsylvania Robert P. Dilworth, mathematician Thomas Dilworth, English cleric Dilworth's theorem in mathematics Dilworth School in Auckland, New Zealand...

König's theorem Menger's theorem (1927) The max-flow min-cut theorem (Ford–Fulkerson algorithm) The Birkhoff–Von Neumann theorem (1946) Dilworth's theorem. In...

largest antichain in a partially ordered set is known as its width. By Dilworth's theorem, this also equals the minimum number of chains (totally ordered subsets)...

of choice. Its applications include extending the four-color theorem and Dilworth's theorem from finite graphs and partially ordered sets to infinite ones...

theorem can be used to prove Dilworth's theorem from the (much easier) proof of Mirsky's theorem, or vice versa. To prove the perfect graph theorem,...

In mathematics, Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under...

important minimax theorems in combinatorics, including Dilworth's theorem and Mirsky's theorem on partially ordered sets, Kőnig's theorem on matchings, and...

known for Dilworth's theorem (Dilworth 1950) relating chains and antichains in partial orders; he was also the first to study antimatroids (Dilworth 1940)...

isomorphism theorem (order theory) Dilworth's theorem (combinatorics, order theory) Four functions theorem (combinatorics) Hahn embedding theorem (ordered...

is Mirsky's theorem, and the perfection of their complements is Dilworth's theorem; these facts, together with the perfect graph theorem can be used to...

such as Hall's marriage theorem and Dilworth's theorem. Since bipartite matching is a special case of maximum flow, the theorem also results from the max-flow...

{\displaystyle n_{1},n_{2},\dots ,n_{p}.} Mathematics portal Dilworth's theorem Erdős–Ko–Rado theorem Anderson, Ian (1987), Combinatorics of Finite Sets, Oxford...

graph Logic gate Boolean analysis Boolean prime ideal theorem Compactness theorem Consensus theorem De Morgan's laws Duality (order theory) Laws of classical...

In mathematics, the Boolean prime ideal theorem states that ideals in a Boolean algebra can be extended to prime ideals. A variation of this statement...

incidence algebras, Sperner's theorem on antichains in power sets, special classes of lattices, valuation rings, and Dilworth's theorem on partitions into chains...

transcendental extensions of the rational numbers. Mirsky's theorem, a dual version of Dilworth's theorem published by Mirsky in 1971, states that in any finite...

theory and model theory, branches of mathematics, Cantor's isomorphism theorem states that every two countable dense unbounded linear orders are order-isomorphic...

& Tamassia (1995a), Theorem 9, p. 118; Baker, Fishburn & Roberts (1971), theorem 4.1, page 18. Garg & Tamassia (1995a), Theorem 15, p. 125; Bertolazzi...

further structure. Another early representation theorem is now known as Stone's representation theorem for distributive lattices (the name honors Marshall...

{\displaystyle (Tu-Tv,u-v)\geq 0\quad \forall u,v\in X.} Kachurovskii's theorem shows that convex functions on Banach spaces have monotonic operators as...

must preserve the existence of least elements. By Cantor's isomorphism theorem, every unbounded countable dense linear order is isomorphic to the ordering...

without the axiom of choice). This issue is discussed in various prime ideal theorems, which are necessary for many applications that require prime ideals. An...

Results Boolean prime ideal theorem Cantor–Bernstein theorem Cantor's isomorphism theorem Dilworth's theorem Dushnik–Miller theorem Hausdorff maximal principle...

Pseudocomplemented lattice Grätzer (1971), Lemma I.6.1, p. 47. Rutherford (1965), Theorem 9.3 p. 25. Stern, Manfred (1999), Semimodular Lattices: Theory and Applications...

Gallai also proved, with Milgram, Dilworth's theorem in 1947, but as they hesitated to publish the result, Dilworth independently discovered and published...

isomorphism from A to a full subcategory of B. Dushnik–Miller theorem Laver's theorem Davey, B. A.; Priestley, H. A. (2002), "Maps between ordered sets"...

set I such that I contains exactly one vertex from each path in P. Dilworth's theorem follows as a corollary of this result. Given a directed graph G, the...