s⋯21. The Erdős–Szekeres theorem can be proved in several different ways; Steele (1995) surveys six different proofs of the Erdős–Szekeres theorem, including...

problem" (so named by Paul Erdős because it led to the marriage of George Szekeres and Esther Klein) is the following statement: Theorem — any set of five points...

theorem relating longest paths and colorings in graphs, and to the Erdős–Szekeres theorem on monotonic subsequences. The height of a partially ordered set...

number Szekeres snark Generalized continued fraction Kruskal–Szekeres coordinates Szekeres–Wilf number Schröder's equation Erdős–Szekeres theorem Obituary...

Robinson-Schensted correspondence can be used to give a simple proof of the Erdős–Szekeres theorem. Viennot's geometric construction, which provides a diagrammatic...

theorem Erdős–Szekeres theorem Erdős–Szemerédi theorem Erdős–Tetali theorem Erdős–Wintner theorem Erdős–Turán inequality Erdős–Ulam problem Erdős–Woods number...

(combinatorics) Erdős–Nagy theorem (discrete geometry) Erdős–Pósa theorem (graph theory) Erdős–Rado theorem (set theory) Erdős–Stone theorem (graph theory) Erdős–Szekeres...

theorems in combinatorics, including Dilworth's theorem and Mirsky's theorem on partially ordered sets, Kőnig's theorem on matchings, and the Erdős–Szekeres...

statement of the theorem to require, in a simple graph, either an r-clique or an s-independent set, see (Gross 2008) or (Erdős & Szekeres 1935). In this...

the form m2i. Therefore, by Dilworth's theorem, the width of this partial order is n. The Erdős–Szekeres theorem on monotone subsequences can be interpreted...

decreasing subsequence of length  s {\displaystyle s} (This is the Erdős–Szekeres theorem). A metric space ( X , d ) {\displaystyle (X,d)} is compact if every...

mathematician Paul Erdős and his various collaborators made many famous mathematical conjectures, over a wide field of subjects, and in many cases Erdős offered...

time by dynamic programming for points in convex position. The Erdős–Szekeres theorem guarantees that every set of n {\displaystyle n} points in general...

which all slopes have the same sign. This is a corollary of the Erdős–Szekeres theorem. Polygonal chains can often be used to approximate more complex...

(1): 264–286, doi:10.1112/plms/s2-30.1.264 (behind a paywall). Erdős, Paul; Szekeres, George (1935), "A combinatorial problem in geometry", Compositio...

O ( n ) {\displaystyle O(n)} term. Example run According to the Erdős–Szekeres theorem, any sequence of n 2 + 1 {\displaystyle n^{2}+1} distinct integers...

and is essentially the same as the coloring number or Szekeres–Wilf number (named after Szekeres and Wilf (1968)). k-degenerate graphs have also been called...

suggested a conjecture offering a modular strengthening of the Erdős–Szekeres theorem proving that the number of points in the interior of the polygon...

Mathematics Paul Erdős and Richard Rado Erdős–Stone theorem Mathematics Paul Erdős and Arthur Harold Stone Erdős–Szekeres theorem Mathematics Paul Erdős and George...

at least to the graph-theoretic reformulation of Ramsey theory by Erdős & Szekeres (1935), the term clique comes from Luce & Perry (1949), who used complete...

761–763, doi:10.2307/2310461, JSTOR 2310461 Szekeres, E.; Szekeres, G. (1965), "On a problem of Schütte and Erdős", The Mathematical Gazette, 49: 290–293...

University Press, pp. 44–46. Morris, Walter D.; Soltan, Valeriu (2000), "The Erdős-Szekeres problem on points in convex position—a survey", Bull. Amer. Math. Soc...

This is the first exponential improvement over the upper bound of Erdős and Szekeres, proved in 1935. Sahasrabudhe has also worked with Marcelo Campos...

early landmark result in the field is the Erdős–Szekeres theorem; in permutation pattern language, the theorem states that for any positive integers a and...

first professor of applied mathematics George Szekeres – mathematician known for the Erdős–Szekeres theorem Ernie Tuck – applied mathematician Mathai Varghese...

4321, 1234 1, 2, 6, 22, 86, 306, 882, 1764, ... A206736 finite Erdős–Szekeres theorem 4312, 1234 1, 2, 6, 22, 86, 321, 1085, 3266, ... A116705 polynomial...

numbers are also known as squareful, square-full, or 2-full. Paul Erdős and George Szekeres studied such numbers and Solomon W. Golomb named such numbers...

{\displaystyle 2a-1} . The coloring number of a graph, also known as its Szekeres-Wilf number (Szekeres & Wilf 1968) is always equal to its degeneracy plus 1 (Jensen...

Made More Relevant to Economics?: An Open Problem, by Eric Maskin The Erdős–Szekeres Problem, by Walter Morris and Valeriu Soltan Novikov’s Conjecture, by...

resulting orbit and its analyticity properties are cogently summarized by Szekeres. Several of the solutions are furnished in terms of asymptotic series,...