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List Of Things Named After Paul Erdős
The following are named after Paul Erdős: * Paul Erdős Award of the World Federation of National Mathematics Competitions * Erdős Prize * Erdős Lectures * Erdős number * Erdős cardinal * Erdős–Nicolas number * Erdős conjecture — a list of numerous conjectures named after Erdős; See also List of conjectures by Paul Erdős. ** Erdős–Turán conjecture on additive bases ** Erdős conjecture on arithmetic progressions ** Erdős discrepancy problem ** Erdős distinct distances problem ** Burr–Erdős conjecture ** Cameron–Erdős conjecture ** Erdős–Faber–Lovász conjecture ** Erdős–Graham conjecture — see Erdős–Graham problem ** Erdős–Hajnal conjecture *Erdós Institute** ** Erdős–Gyárfás conjecture ** Erdős–Straus conjecture ** Erdős sumset conjecture ** Erdős–Szekeres conjecture ** Erdős–Turán conjecture ** Erdős–Turán conjecture on additive bases * Copeland–Erdős constant * Erdős–Tenenbaum–Ford constant * Erdős� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Erdős
Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 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, graph theory, number theory, mathematical analysis, approximation theory, set theory, and probability theory. Much of his work centered around discrete mathematics, cracking many previously unsolved problems in the field. He championed and contributed to Ramsey theory, which studies the conditions in which order necessarily appears. Overall, his work leaned towards solving previously open problems, rather than developing or exploring new areas of mathematics. Erdős published around 1,500 mathematical papers during his lifetime, a figure that remains unsurpassed. He firmly believed mathematics to be a social activity, living an itinerant lifestyle with the sole purpose of writing mathematical papers with other mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, have the property that every pair of complete graphs has at most one shared vertex, then the union of the graphs can be properly colored with colors. A proof of the conjecture for all sufficiently large values of was announced in 2021 by Dong Yeap Kang, Tom Kelly, Daniela Kühn, Abhishek Methuku, and Deryk Osthus. Equivalent formulations introduced the problem with a story about seating assignment in committees: suppose that, in a university department, there are committees, each consisting of faculty members, and that all committees meet in the same room, which has chairs. Suppose also that at most one person belongs to the intersection of any two committees. Is it possible to assign the committee members to chairs in such a way ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 vertices. It is named after Paul Erdős and Louis Mordell. posed the problem of proving the inequality; a proof was provided two years later by . This solution was however not very elementary. Subsequent simpler proofs were then found by , , and . Barrow's inequality is a strengthened version of the Erdős–Mordell inequality in which the distances from ''P'' to the sides are replaced by the distances from ''P'' to the points where the angle bisectors of ∠''APB'', ∠''BPC'', and ∠''CPA'' cross the sides. Although the replaced distances are longer, their sum is still less than or equal to half the sum of the distances to the vertices. Statement Let P be an arbitrary point P inside a given triangle ABC, and let PL, PM, and PN b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 graph theory, it can be described as a complete graph with vertices located on the integer square grid \mathbb^2 such that all mutual distances between the vertices are integers, while all other grid points have a non-integer distance to at least one vertex. Erdős–Diophantine graphs are named after Paul Erdős and Diophantus of Alexandria. They form a subset of the set of Diophantine figures, which are defined as complete graphs in the Diophantine plane for which the length of all edges are integers (unit distance graph In mathematics, particularly geometric graph theory, a unit distance graph is a graph formed from a collection of points in the Euclidean plane by connecting two points whenever the distance between them is exact ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős–Borwein Constant
The Erdős–Borwein constant is the sum of the reciprocals of the Mersenne numbers. It is named after Paul Erdős and Peter Borwein. By definition it is: :E=\sum_^\frac\approx1.606695152415291763\dots Equivalent forms It can be proven that the following forms all sum to the same constant: : E=\sum_^\frac\frac : E=\sum_^\sum_^ \frac : E=1+\sum_^ \frac : E=\sum_^\frac where σ0(''n'') = ''d''(''n'') is the divisor function, a multiplicative function that equals the number of positive divisors of the number ''n''. To prove the equivalence of these sums, note that they all take the form of Lambert series and can thus be resummed as such. Irrationality Erdős in 1948 showed that the constant ''E'' is an irrational number. Later, Borwein provided an alternative proof. Despite its irrationality, the binary representation of the Erdős–Borwein constant may be calculated efficiently. Applications The Erdős–Borwein constant comes up in the average case analysis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős–Bacon Number
A person's Erdős–Bacon number is the sum of one's Erdős number—which measures the "collaborative distance" in authoring academic papers between that person and Hungarian mathematician Paul Erdős—and one's Bacon number—which represents the number of links, through roles in films, by which the person is separated from American actor Kevin Bacon. The lower the number, the closer a person is to Erdős and Bacon, which reflects a small world phenomenon in academia and entertainment. To have a defined Erdős–Bacon number, it is necessary to have both appeared in a film and co-authored an academic paper, although this in and of itself is not sufficient as ones co-authors must have a known chain leading to Paul Erdős, and one's film must have actors eventually leading to Kevin Bacon. Academic scientists Mathematician Daniel Kleitman has an Erdős–Bacon number of 3. He co-authored papers with Erdős and has a Bacon number of 2 via Minnie Driver in '' Good Will Hunting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős–Tenenbaum–Ford Constant
The Erdős–Tenenbaum–Ford constant is a mathematical constant that appears in number theory. Named after mathematicians Paul Erdős, Gérald Tenenbaum, and Kevin Ford, it is defined as :\delta := 1 - \frac = 0.0860713320\dots where \log is the natural logarithm. Following up on earlier work by Tenenbaum, Ford used this constant in analyzing the number H(x,y,z) of integers that are at most x and that have a divisor in the range ,z/math>. Multiplication table problem For each positive integer N, let M(N) be the number of distinct integers in an N \times N multiplication table. In 1960, Erdős studied the asymptotic behavior of M(N) and proved that :M(N) = \frac, as N \to +\infty. References External links Decimal digits of the Erdős–Tenenbaum–Ford constanton the OEIS The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences. It was created and maintained by Neil Sloane while researching at AT&T Labs. He transferred the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 irrational; this can be proven with Dirichlet's theorem on arithmetic progressions or Bertrand's postulate (Hardy and Wright, p. 113) or Ramare's theorem that every even integer is a sum of at most six primes. It also follows directly from its normality (see below). By a similar argument, any constant created by concatenating "0." with all primes in an arithmetic progression ''dn'' + ''a'', where ''a'' is coprime to ''d'' and to 10, will be irrational; for example, primes of the form 4''n'' + 1 or 8''n'' + 1. By Dirichlet's theorem, the arithmetic progression ''dn'' · 10''m'' + ''a'' contains primes for all ''m'', and those primes are also in ''cd'' + ''a'', so the con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős–Szekeres Conjecture
In mathematics, the "happy ending problem" (so named by Paul Erdős because it led to the marriage of George Szekeres and Esther Szekeres, Esther Klein) is the following statement: This was one of the original results that led to the development of Ramsey theory. The happy ending theorem can be proven by a simple case analysis: if four or more points are vertices of the convex hull, any four such points can be chosen. If on the other hand, the convex hull has the form of a triangle with two points inside it, the two inner points and one of the triangle sides can be chosen. See for an illustrated explanation of this proof, and for a more detailed survey of the problem. The Erdős–Szekeres conjecture states precisely a more general relationship between the number of points in a general-position point set and its largest subset forming a convex polygon, namely that the smallest number of points for which any general position arrangement contains a convex subset of n points i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős Sumset Conjecture
In additive combinatorics, the Erdős sumset conjecture is a conjecture which states that if a subset A of the natural numbers \mathbb has a positive upper density then there are two infinite subsets B and C of \mathbb such that A contains the sumset B+C. It was posed by Paul Erdős, and was proven in 2019 in a paper by Joel Moreira, Florian Richter and Donald Robertson. 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 ... Notes Conjectures Conjectures that have been proved Paul Erdős Combinatorics {{combin-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erdős–Straus Conjecture
The Erdős–Straus conjecture is an unproven statement in number theory. The conjecture is that, for every integer n that is 2 or more, there exist positive integers x, y, and z for which \frac=\frac+\frac+\frac. In other words, the number 4/n can be written as a sum of three positive unit fractions. The conjecture is named after Paul Erdős and Ernst G. Straus, who formulated it in 1948, but it is connected to much more ancient mathematics; sums of unit fractions, like the one in this problem, are known as Egyptian fractions, because of their use in ancient Egyptian mathematics. The Erdős–Straus conjecture is one of many conjectures by Erdős, and one of many unsolved problems in mathematics concerning Diophantine equations. Although a solution is not known for all values of , infinitely many values in certain infinite arithmetic progressions have simple formulas for their solution, and skipping these known values can speed up searches for counterexamples. Additionally, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
