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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 conjecture on cycles with lengths equal to a power of two in graphs with minimum degree 3. * The Erdős–Hajnal conjecture that in a family of graphs defined by an excluded induced subgraph, every graph has either a large clique or a large independent set. * The Erdős–Mollin–Walsh conjecture on consecutive triples of powerful numbers. * The Erdős–Selfridge conjecture that a covering system with distinct moduli contains at least one even modulus. * The Erdős–Straus conjecture on the Diophantine equation 4/''n'' = 1/''x'' + 1/''y'' + 1/''z''. * The Erdős conjecture on arithmetic progressions in sequences with divergent sums of reciprocals. * The Erdős–Szekeres conjecture on the number of points needed to ensure that a point ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagoreans, Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The London Mathematical Society
The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical Society and the Operational Research Society (ORS). History The Society was established on 16 January 1865, the first president being Augustus De Morgan. The earliest meetings were held in University College, but the Society soon moved into Burlington House, Piccadilly. The initial activities of the Society included talks and publication of a journal. The LMS was used as a model for the establishment of the American Mathematical Society in 1888. Mary Cartwright was the first woman to be President of the LMS (in 1961–62). The Society was granted a royal charter in 1965, a century after its foundation. In 1998 the Society moved from rooms in Burlington House into De Morgan House (named after the society's first president), a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
András Sárközy
András Sárközy (born in Budapest) is a Hungarian mathematician, working in analytic and combinatorial number theory, although his first works were in the fields of geometry and classical analysis. He has the largest number of papers co-authored with Paul Erdős (a total of 62); he has an Erdős number of one. He proved the Furstenberg–Sárközy theorem that every sequence of natural numbers with positive upper density contains two members whose difference is a full square. He was elected a corresponding member (1998), and a full member (2004) of the Hungarian Academy of Sciences. He received the Széchenyi Prize (2010). He is the father of the mathematician Gábor N. Sárközy Gábor N. Sárközy, also known as Gabor Sarkozy, is a Hungarian-American mathematician, the son of noted mathematician András Sárközy. He is currently on faculty of the Computer Science Department at Worcester Polytechnic Institute, MA, Unite .... References * {{DEFAULTSORT:Sarkozy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Furstenberg–Sárközy Theorem
In mathematics, a square-difference-free set is a set of natural numbers, no two of which differ by a square number. Hillel Furstenberg and András Sárközy proved in the late 1970s the Furstenberg–Sárközy theorem of additive number theory showing that, in a certain sense, these sets cannot be very large. In the game of subtract a square, the positions where the next player loses form a square-difference-free set. Another square-difference-free set is obtained by doubling the Moser–de Bruijn sequence. The best known upper bound on the size of a square-difference-free set of numbers up to n is only slightly sublinear, but the largest known sets of this form are significantly smaller, of size \approx n^. Closing the gap between these upper and lower bounds remains an open problem. The sublinear size bounds on square-difference-free sets can be generalized to sets where certain other polynomials are forbidden as differences between pairs of elements. Example An exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hajnal–Szemerédi Theorem
In graph theory, an area of mathematics, an equitable coloring is an assignment of colors to the vertices of an undirected graph, in such a way that *No two adjacent vertices have the same color, and *The numbers of vertices in any two color classes differ by at most one. That is, the partition of vertices among the different colors is as uniform as possible. For instance, giving each vertex a distinct color would be equitable, but would typically use many more colors than are necessary in an optimal equitable coloring. An equivalent way of defining an equitable coloring is that it is an embedding of the given graph as a subgraph of a Turán graph with the same set of vertices. There are two kinds of chromatic number associated with equitable coloring.. The equitable chromatic number of a graph ''G'' is the smallest number ''k'' such that ''G'' has an equitable coloring with ''k'' colors. But ''G'' might not have equitable colorings for some larger numbers of colors; the equita ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Endre Szemerédi
Endre Szemerédi (; born August 21, 1940) is a Hungarian-American mathematician and computer scientist, working in the field of combinatorics and theoretical computer science. He has been the State of New Jersey Professor of computer science at Rutgers University since 1986. He also holds a professor emeritus status at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences. Szemerédi has won prizes in mathematics and science, including the Abel Prize in 2012. He has made a number of discoveries in combinatorics and computer science, including Szemerédi's theorem, the Szemerédi regularity lemma, the Erdős–Szemerédi theorem, the Hajnal–Szemerédi theorem and the Szemerédi–Trotter theorem. Early life Szemerédi was born in Budapest. Since his parents wished him to become a doctor, Szemerédi enrolled at a college of medicine, but he dropped out after six months (in an interview he explained it: "I was not sure I could do work bearing such res ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
András Hajnal
András Hajnal (May 13, 1931 – July 30, 2016) was a professor of mathematics at Rutgers University and a member of the Hungarian Academy of Sciences known for his work in set theory and combinatorics. Biography Hajnal was born on 13 May 1931,Curriculum vitae in , . He received his university diploma (M.Sc. degree) in 1953 from the , his |
Equitable Coloring
In graph theory, an area of mathematics, an equitable coloring is an assignment of colors to the vertices of an undirected graph, in such a way that *No two adjacent vertices have the same color, and *The numbers of vertices in any two color classes differ by at most one. That is, the partition of vertices among the different colors is as uniform as possible. For instance, giving each vertex a distinct color would be equitable, but would typically use many more colors than are necessary in an optimal equitable coloring. An equivalent way of defining an equitable coloring is that it is an embedding of the given graph as a subgraph of a Turán graph with the same set of vertices. There are two kinds of chromatic number associated with equitable coloring.. The equitable chromatic number of a graph ''G'' is the smallest number ''k'' such that ''G'' has an equitable coloring with ''k'' colors. But ''G'' might not have equitable colorings for some larger numbers of colors; the equitabl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Burr–Erdős Conjecture
In mathematics, the Burr–Erdős conjecture was a problem concerning the Ramsey number of sparse graphs. The conjecture is named after Stefan Burr and Paul Erdős, and is one of many conjectures named after Erdős; it states that the Ramsey number of graphs in any sparse family of graphs should grow linearly in the number of vertices of the graph. The conjecture was proven by Choongbum Lee. Thus it is now a theorem. Definitions If ''G'' is an undirected graph, then the degeneracy of ''G'' is the minimum number ''p'' such that every subgraph of ''G'' contains a vertex of degree ''p'' or smaller. A graph with degeneracy ''p'' is called ''p''-degenerate. Equivalently, a ''p''-degenerate graph is a graph that can be reduced to the empty graph by repeatedly removing a vertex of degree ''p'' or smaller. It follows from Ramsey's theorem that for any graph ''G'' there exists a least integer r(G), the ''Ramsey number'' of ''G'', such that any complete graph on at least r(G) vertices ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. Th ... [...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] |
