In mathematics, in the areas of order theory and combinatorics, Mirsky's theorem characterizes the height of any finite partially ordered set in terms...

in number theory, linear algebra, and combinatorics. Mirsky's theorem is named after him. Mirsky was born in Russia on 19 December 1918 to a medical family...

may be partitioned. This is called Mirsky's theorem. Its proof is much simpler than the proof of Dilworth's theorem itself: for any element x, consider...

novelist Steve Mirsky, American journalist Mirsky's theorem Mirsky's Worst of the Web Boris Mirski Gallery Mirskis, a surname Svyatopolk-Mirsky This page lists...

partially ordered set (the length of its longest chain) equals by Mirsky's theorem the minimum number of antichains into which the set can be partitioned...

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...

result is referred to as the matrix approximation lemma or Eckart–Young–Mirsky theorem. This problem was originally solved by Erhard Schmidt in the infinite...

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

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...

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 ordering...

graphs 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...

{\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...

In set theory and order theory, the Cantor–Bernstein theorem states that the cardinality of the second type class, the class of countable order types...

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

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

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...

countable intersections of open sets are open Speer 2007, Theorem 7. Arenas 1999, Theorem 2.2. Erné, M. "The ABC of order and topology" (PDF)., page...

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

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

axiom of choice). The principle is also called the Hausdorff maximality theorem or the Kuratowski lemma (Kelley 1955:33). The Hausdorff maximal principle...

maximal principle Knaster–Tarski theorem Kruskal's tree theorem Laver's theorem Mirsky's theorem Szpilrajn extension theorem Zorn's lemma Properties & Types (list)...

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

G {\displaystyle G} is acyclic, this can also be seen as a form of Mirsky's theorem that the longest chain in a partially ordered set equals the minimum...

and a balanced assignment of vertices to layers. For instance, by Mirsky's theorem, assigning vertices by layers according to the length of the longest...

a wqo (Nash-Williams' theorem). Embedding between countable scattered linear order types is a well-quasi-order (Laver's theorem). Embedding between countable...

number, called the order type of the well-ordered set. The well-ordering theorem, which is equivalent to the axiom of choice, states that every set can...

maximal principle Knaster–Tarski theorem Kruskal's tree theorem Laver's theorem Mirsky's theorem Szpilrajn extension theorem Zorn's lemma Properties & Types (list)...

maximal principle Knaster–Tarski theorem Kruskal's tree theorem Laver's theorem Mirsky's theorem Szpilrajn extension theorem Zorn's lemma Properties & Types (list)...

more abstract approach makes much sense, because one can derive numerous theorems in the general setting, without focusing on the details of any particular...