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Beck–Fiala Theorem
In mathematics, the Beck–Fiala theorem is a major theorem in discrepancy theory due to József Beck József Beck (Budapest, Hungary, February 14, 1952) is a Harold H. Martin Professor of Mathematics at Rutgers University. His contributions to combinatorics include the partial colouring lemma and the Beck–Fiala theorem in '' discrepancy th ... and Tibor Fiala. Discrepancy is concerned with coloring elements of a ground set such that each set in a certain set system is as balanced as possible, i.e., has approximately the same number of elements of each color. The Beck–Fiala theorem is concerned with the case where each element doesn't appear many times across all sets. The theorem guarantees that if each element appears at most times, then the elements can be colored so that the imbalance is at most . Statement Formally, given a universe : = \ and a collection of subsets : S_1, S_2, \ldots, S_m \subseteq /math> such that for each i \in /math>, : \vert \ \vert ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrepancy Theory
In mathematics, discrepancy theory describes the deviation of a situation from the state one would like it to be in. It is also called the theory of irregularities of distribution. This refers to the theme of ''classical'' discrepancy theory, namely distributing points in some space such that they are evenly distributed with respect to some (mostly geometrically defined) subsets. The discrepancy (irregularity) measures how far a given distribution deviates from an ideal one. Discrepancy theory can be described as the study of inevitable irregularities of distributions, in measure-theoretic and combinatorial settings. Just as Ramsey theory elucidates the impossibility of total disorder, discrepancy theory studies the deviations from total uniformity. A significant event in the history of discrepancy theory was the 1916 paper of Weyl on the uniform distribution of sequences in the unit interval. __NOTOC__ Theorems Discrepancy theory is based on the following classic theorems: * T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
József Beck
József Beck (Budapest, Hungary, February 14, 1952) is a Harold H. Martin Professor of Mathematics at Rutgers University. His contributions to combinatorics include the partial colouring lemma and the Beck–Fiala theorem in ''discrepancy theory'', the algorithmic version of the Lovász local lemma, the Beck's theorem (geometry), two extremes theorem in combinatorial geometry and the second moment method in the theory of positional games, among others. Beck was awarded the Fulkerson Prize in 1985 for a paper titled ''"Roth's estimate of the discrepancy of integer sequences is nearly sharp"'', which introduced the notion of discrepancy on hypergraphs and established an upper bound on the discrepancy of the family of arithmetic progressions contained in , matching the classical lower bound up to a polylogarithmic function, polylogarithmic factor. Jiří Matoušek (mathematician), Jiří Matoušek and Joel Spencer later succeeded in getting rid of this factor, showing that the bound ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tibor Fiala
Tibor is a masculine given name found throughout Europe. There are several explanations for the origin of the name: * from Latin name Tiberius, which means "from Tiber", Tiber being a river in Rome. * in old Slavic languages, Tibor means "sacred place". * shortened form of the name ''Tiborc''; which originates from the ancient Latin surname Tiburtius. * from Etruscan name Tibur, which means "honest man" Some notable men known by this name include: * Tibor Antalpéter * Tibor Benedek * Tibor Farkas * Tibor Feheregyhazi * Tibor Fischer * Tibor Gécsek * Tibor Hollo * Tibor Kalman * Tibor R. Machan * Tibor Mičinec * Tibor Nyilasi * Tibor Ordina * Tibor Parák * Tibor Pleiß * Tibor Radó * Tibor Renyi * Tibor Selymes * Tibor Stark * Tibor Szasz * Tibor Szele * Tibor Varga (ice hockey) * Tibor Varga (violinist) * Tibor Zsitvay See also * Ctibor (name) * ''Tibor'' is the Hungarian name for Tibru village, Cricău Commune, Alba County, Romania * TIBOR Tibor is a masculine given nam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
