The following are named after

Paul Erdős Paul Erdős ( ; 26March 191320September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, g ...

Theorems

* de Bruijn–Erdős theorem (graph theory) *

de Bruijn–Erdős theorem (incidence geometry) In incidence geometry, the De Bruijn–Erdős theorem, originally published by Nicolaas Govert de Bruijn and Paul Erdős in 1948, states a lower bound on the number of lines determined by ''n'' points in a projective plane. By duality, this is ...

* Davenport–Erdős theorem *

Erdős–Anning theorem The Erdős–Anning theorem states that, whenever an Infinite set, infinite number of points in the plane all have integer distances, the points lie on a straight line. The same result holds in higher dimensional Euclidean spaces. The theorem ca ...

* Erdős–Beck theorem * Erdős–Dushnik–Miller theorem * Erdős–Fuchs theorem *

Erdős–Gallai theorem The Erdős–Gallai theorem is a result in graph theory, a branch of combinatorial mathematics. It provides one of two known approaches to solving the graph realization problem, i.e. it gives a necessary and sufficient condition for a finite seque ...

Erdős–Ginzburg–Ziv theorem In number theory, zero-sum problems are certain kinds of combinatorial problems about the structure of a finite abelian group. Concretely, given a finite abelian group ''G'' and a positive integer ''n'', one asks for the smallest value of ''k'' s ...

Erdős–Kac theorem In number theory, the Erdős–Kac theorem, named after Paul Erdős and Mark Kac, and also known as the fundamental theorem of probabilistic number theory, states that if ''ω''(''n'') is the number of distinct prime factors of ''n'', then, loosely ...

Erdős–Kaplansky theorem The Erdős–Kaplansky theorem is a theorem from functional analysis. The theorem makes a fundamental statement about the dimension of the dual spaces of infinite-dimensional vector spaces; in particular, it shows that the algebraic dual space is ...

Erdős–Ko–Rado theorem In mathematics, the Erdős–Ko–Rado theorem limits the number of Set (mathematics), sets in a family of sets for which every two sets have at least one element in common. Paul Erdős, Chao Ko, and Richard Rado proved the theorem in 1938, but d ...

* Erdős–Nagy theorem *

Erdős–Pósa theorem In the mathematical discipline of graph theory, the Erdős–Pósa theorem, named after Paul Erdős and Lajos Pósa, relates two parameters of a graph: * The size of the largest collection of vertex-disjoint cycles contained in the graph; * The s ...

Erdős–Rado theorem In partition calculus, part of combinatorial set theory, a branch of mathematics, the Erdős–Rado theorem is a basic result extending Ramsey's theorem to uncountable sets. It is named after Paul Erdős and Richard Rado. It is sometimes also a ...

Erdős–Stone theorem In extremal graph theory, the Erdős–Stone theorem is an asymptotic result generalising Turán's theorem to bound the number of edges in an ''H''-free graph for a non-complete graph ''H''. It is named after Paul Erdős and Arthur Stone (mathemati ...

Erdős–Szekeres theorem In mathematics, the Erdős–Szekeres theorem asserts that, given ''r'', ''s,'' any sequence of distinct real numbers with length at least (''r'' − 1)(''s'' − 1) + 1 contains a monotonically increasing sub ...

Erdős–Szemerédi theorem In arithmetic combinatorics, the Erdős–Szemerédi theorem states that for every finite set of integers, at least one of the sets and (the sets of pairwise sums and pairwise products, respectively) form a significantly larger set. More precis ...

Erdős–Tetali theorem In additive number theory, an area of mathematics, the Erdős–Tetali theorem is an existence theorem concerning economical additive basis, additive bases of every order. More specifically, it states that for every fixed integer h \geq 2, there exi ...

* Erdős–Wintner theorem *

Erdős–Mordell inequality In Euclidean geometry, the Erdős–Mordell inequality states that for any triangle ''ABC'' and point ''P'' inside ''ABC'', the sum of the distances from ''P'' to the sides is less than or equal to half of the sum of the distances from ''P'' to the ...

* Chung–Erdős inequality *

Erdős–Turán inequality In mathematics, the Erdős–Turán inequality bounds the distance between a probability measure on the circle and the Lebesgue measure, in terms of Fourier coefficients. It was proved by Paul Erdős and Pál Turán in 1948. Let ''μ'' be a probab ...

Hsu–Robbins–Erdős theorem In the mathematical theory of probability, the Hsu–Robbins–Erdős theorem states that if X_1, \ldots ,X_n is a sequence of i.i.d. random variables with zero mean and finite variance and : S_n = X_1 + \cdots + X_n, \, then : \sum\limits_ P ...

Erdős arcsine law Erdős, Erdos, or Erdoes is a Hungarian surname. Paul Erdős (1913–1996), Hungarian mathematician Other people with the surname * Ágnes Erdős (1950–2021), Hungarian politician * Brad Erdos (born 1990), Canadian football player * Éva Erd� ...

Conjectures

Erdős conjecture Erdős, Erdos, or Erdoes is a Hungarian surname. Paul Erdős (1913–1996), Hungarian mathematician Other people with the surname * Ágnes Erdős (1950–2021), Hungarian politician * Brad Erdos (born 1990), Canadian football player * Éva Erd� ...

— a list of numerous conjectures named after Erdős; See also

List of conjectures by Paul Erdős The prolific mathematician Paul Erdős and his various collaborators made many famous mathematical conjectures, over a wide field of subjects, and in many cases Erdős offered monetary rewards for solving them. Unsolved * The Erdős–Gyárfás c ...

. **

Erdős–Turán conjecture on additive bases The Erdős–Turán conjecture is an old unsolved problem in additive number theory (not to be confused with Erdős conjecture on arithmetic progressions) posed by Paul Erdős and Pál Turán in 1941. It concerns additive bases, subsets of natu ...

Erdős conjecture on arithmetic progressions Erdős' conjecture on arithmetic progressions, often referred to as the Erdős–Turán conjecture, is a conjecture in arithmetic combinatorics (not to be confused with the Erdős–Turán conjecture on additive bases). It states that if the sum ...

Erdős discrepancy problem In mathematics, a sign sequence, or ±1–sequence or bipolar sequence, is a sequence of numbers, each of which is either 1 or −1. One example is the sequence (1, −1, 1, −1, ...). Such sequences are commonly studied in discrepancy theo ...

Erdős distinct distances problem In discrete geometry, the Erdős distinct distances problem states that every set of points in the plane has a nearly-linear number of distinct distances. It was posed by Paul Erdős in 1946 and almost proven by Larry Guth and Nets Katz in 2015. ...

** Burr–Erdős conjecture **

Cameron–Erdős conjecture In combinatorics, the Cameron–Erdős conjecture (now a theorem) is the statement that the number of sum-free sets contained in = \ is O\big(\big). The sum of two odd numbers is even, so a set of odd numbers is always sum-free. There are \lce ...

Erdős–Faber–Lovász conjecture In graph theory, the Erdős–Faber–Lovász conjecture is a problem about graph coloring, named after Paul Erdős, Vance Faber, and László Lovász, who formulated it in 1972.. It says: :If complete graphs, each having exactly vertices, ha ...

** Erdős–Graham conjecture — see

Erdős–Graham problem In combinatorial number theory, the Erdős–Graham problem is the problem of proving that, if the set \ of integers greater than one is partitioned into finitely many subsets, then one of the subsets can be used to form an Egyptian fraction repre ...

Erdős–Hajnal conjecture In graph theory, a branch of mathematics, the Erdős–Hajnal conjecture states that families of graphs defined by forbidden induced subgraphs have either large cliques or large independent sets. It is named for Paul Erdős and András Hajnal, wh ...

Erdős–Gyárfás conjecture In graph theory, the unproven Erdős–Gyárfás conjecture, made in 1995 by mathematician Paul Erdős and his collaborator András Gyárfás, states that every graph with minimum degree 3 contains a simple cycle whose length is a power of two. ...

Erdős–Straus conjecture The Erdős–Straus conjecture is an unproven statement in number theory. The conjecture is that, for every integer n that is greater than or equal to 2, there exist positive integers x, y, and z for which \frac=\frac+\frac+\frac. In other word ...

** Erdős sumset conjecture ** Erdős–Szekeres conjecture ** Erdős–Turán conjecture (disambiguation) **

Erdős–Ulam problem In mathematics, the Erdős–Ulam problem asks whether the plane contains a dense set of points whose Euclidean distances are all rational numbers. It is named after Paul Erdős and Stanislaw Ulam. Large point sets with rational distances The Erd ...

** Erdős–Moser equation

Definitions

* Erdős cardinal * Erdős–Nicolas number *

Erdős–Diophantine graph An Erdős–Diophantine graph is an object in the mathematical subject of Diophantine equations consisting of a set of integer points at integer distances in the plane that cannot be extended by any additional points. Equivalently, in geometric ...

Erdős–Rényi model In the mathematical field of graph theory, the Erdős–Rényi model refers to one of two closely related models for generating random graphs or the evolution of a random network. These models are named after Hungarians, Hungarian mathematicians ...

Erdős space Erdős, Erdos, or Erdoes is a Hungarian surname. Paul Erdős (1913–1996), Hungarian mathematician Other people with the surname * Ágnes Erdős (1950–2021), Hungarian politician * Brad Erdos (born 1990), Canadian football player * Éva ...

Erdős–Woods number In number theory, a positive integer is said to be an Erdős–Woods number if it has the following property: there exists a positive integer such that in the sequence of consecutive integers, each of the elements has a non-trivial common fac ...

Constants

Copeland–Erdős constant The Copeland–Erdős constant is the concatenation of "0." with the base 10 representations of the prime numbers in order. Its value, using the modern definition of prime, is approximately :0.235711131719232931374143... . The constant is irratio ...

* Erdős–Tenenbaum–Ford constant

Other

Erdős number The Erdős number () describes the "collaborative distance" between mathematician Paul Erdős and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a particular individual ...

Erdős–Bacon number A person's Erdős–Bacon number is the sum of their Erdős number—which measures the "collaborative distance" in authoring academic papers between that person and Hungarian mathematician Paul Erdős—and their Bacon number—which represents t ...

Erdős Prize The Anna and Lajos Erdős Prize in Mathematics is a prize given by the Israel Mathematical Union to an Israeli mathematician (in any field of mathematics and computer science), "with preference to candidates up to the age of 40." The prize was e ...

Erdős Lectures Erdős Lectures in Discrete Mathematics and Theoretical Computer Science is a distinguished lecture series at Hebrew University of Jerusalem named after mathematician Paul Erdős. It is bringing an outstanding mathematician or computer scientist to ...

Paul Erdős Award The Paul Erdős Award, named after Paul Erdős, is given by the World Federation of National Mathematics Competitions for those who "have played a significant role in the development of mathematical challenges at the national or international le ...

of the World Federation of National Mathematics Competitions

External links

Erdős Institute

Erdős Website
— Collection of Mathematical Problems. * Erdőspál — Asteroid. {{DEFAULTSORT:List of things named after Paul Erdos Erdos Paul Erdős