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Lam's Problem
In finite geometry, Lam's problem is the problem of determining if a finite projective plane of order ten exists. The order ten case is the first theoretically uncertain case, as all smaller orders can be resolved by purely theoretical means. Lam's problem is named after Clement W. H. Lam who experimentally determined that projective planes of order ten do not exist via exhaustive computational searches. Introduction A finite projective plane of order n is a collection of points and lines such that * any two points define a unique line, * any two lines meet at a unique point, * there are exactly n+1 points on every line, and * there are exactly n+1 lines through every point. A consequence of this definition is that a projective plane of order n will contain n^2+n+1 points and n^2+n+1 lines. The incidence relation between points and lines may equivalently be described using an incidence matrix. In this context a projective plane of order n is equivalent to a (n^2+n+1)\times(n^2+ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Geometry
Finite is the opposite of infinite. It may refer to: * Finite number (other) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb Traditionally, a finite verb (from la, fīnītus, past participle of to put an end to, bound, limit) is the form "to which number and person appertain", in other words, those inflected for number and person. Verbs were originally said to be '' ..., a verb form that has a subject, usually being inflected or marked for person and/or tense or aspect * "Finite", a song by Sara Groves from the album '' Invisible Empires'' See also * * Nonfinite (other) {{disambiguation fr:Fini it:Finito ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamming Weight
The Hamming weight of a string is the number of symbols that are different from the zero-symbol of the alphabet used. It is thus equivalent to the Hamming distance from the all-zero string of the same length. For the most typical case, a string of bits, this is the number of 1's in the string, or the digit sum of the binary representation of a given number and the ''ℓ''₁ norm of a bit vector. In this binary case, it is also called the population count, popcount, sideways sum, or bit summation. History and usage The Hamming weight is named after Richard Hamming although he did not originate the notion. The Hamming weight of binary numbers was already used in 1899 by James W. L. Glaisher to give a formula for the number of odd binomial coefficients in a single row of Pascal's triangle. Irving S. Reed introduced a concept, equivalent to Hamming weight in the binary case, in 1954. Hamming weight is used in several disciplines including information theory, coding theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AAAI Conference On Artificial Intelligence
The AAAI Conference on Artificial Intelligence (AAAI) is one of the leading international academic conference in artificial intelligence held annually. Along with ICML, NeurIPS and ICLR, it is one of the primary conferences of high impact in machine learning and artificial intelligence research. It is supported by the Association for the Advancement of Artificial Intelligence. Precise dates vary from year to year, but paper submissions are generally due at the end of August to beginning of September, and the conference is generally held during the following February. The first AAAI was held in 1980 at Stanford University, Stanford California. During AAAI-20 conference, AI pioneers and 2018 Turing Award winners Yann LeCun and Yoshua Bengio among eight other researchers were honored as the AAAI 2020 Fellows. Along with other conferences such as NeurIPS, ICML, AAAI uses artificial intelligence algorithm to assign papers to reviewers. Locations * AAAI-2023 Washington Convention ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SAT Solver
The SAT ( ) is a standardized test widely used for college admissions in the United States. Since its debut in 1926, its name and scoring have changed several times; originally called the Scholastic Aptitude Test, it was later called the Scholastic Assessment Test, then the SAT I: Reasoning Test, then the SAT Reasoning Test, then simply the SAT. The SAT is wholly owned, developed, and published by the College Board, a private, not-for-profit organization in the United States. It is administered on behalf of the College Board by the Educational Testing Service, which until recently developed the SAT as well. The test is intended to assess students' readiness for college. The SAT was originally designed not to be aligned with high school curricula, but several adjustments were made for the version of the SAT introduced in 2016, and College Board president David Coleman has said that he also wanted to make the test reflect more closely what students learn in high school with the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canadian Journal Of Mathematics
The ''Canadian Journal of Mathematics'' (french: Journal canadien de mathématiques) is a bimonthly mathematics journal published by the Canadian Mathematical Society. It was established in 1949 by H. S. M. Coxeter and G. de B. Robinson. The current editors-in-chief of the journal are Louigi Addario-Berry and Eyal Goren. The journal publishes articles in all areas of mathematics. See also * Canadian Mathematical Bulletin References External links * University of Toronto Press academic journals Mathematics journals Publications established in 1949 Bimonthly journals Multilingual journals Cambridge University Press academic journals Academic journals associated with learned and professional societies of Canada {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cray-1
The Cray-1 was a supercomputer designed, manufactured and marketed by Cray Research. Announced in 1975, the first Cray-1 system was installed at Los Alamos National Laboratory in 1976. Eventually, over 100 Cray-1s were sold, making it one of the most successful supercomputers in history. It is perhaps best known for its unique shape, a relatively small C-shaped cabinet with a ring of benches around the outside covering the power supplies and the cooling system. The Cray-1 was the first supercomputer to successfully implement the vector processor design. These systems improve the performance of math operations by arranging memory and registers to quickly perform a single operation on a large set of data. Previous systems like the CDC STAR-100 and ASC had implemented these concepts but did so in a way that seriously limited their performance. The Cray-1 addressed these problems and produced a machine that ran several times faster than any similar design. The Cray-1's architect w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Mathematics (journal)
''Discrete Mathematics'' is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications. It was established in 1971 and is published by North-Holland Publishing Company. It publishes both short notes, full length contributions, as well as survey articles. In addition, the journal publishes a number of special issues each year dedicated to a particular topic. Although originally it published articles in French and German, it now allows only English language articles. The editor-in-chief is Douglas West ( University of Illinois, Urbana). History The journal was established in 1971. The very first article it published was written by Paul Erdős, who went on to publish a total of 84 papers in the journal. Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 0.87. Notable publications * The 1972 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Combinatorial Theory
The ''Journal of Combinatorial Theory'', Series A and Series B, are mathematical journals specializing in combinatorics and related areas. They are published by Elsevier. ''Series A'' is concerned primarily with structures, designs, and applications of combinatorics. ''Series B'' is concerned primarily with graph and matroid theory. The two series are two of the leading journals in the field and are widely known as ''JCTA'' and ''JCTB''. The journal was founded in 1966 by Frank Harary and Gian-Carlo Rota.They are acknowledged on the journals' title pages and Web sites. SeEditorial board of JCTA Originally there was only one journal, which was split into two parts in 1971 as the field grew rapidly. An electronic, |
Enumerator Polynomial
In coding theory, the weight enumerator polynomial of a binary linear code specifies the number of words of each possible Hamming weight. Let C \subset \mathbb_2^n be a binary linear code length n. The weight distribution is the sequence of numbers : A_t = \#\ giving the number of codewords ''c'' in ''C'' having weight ''t'' as ''t'' ranges from 0 to ''n''. The weight enumerator is the bivariate polynomial : W(C;x,y) = \sum_^n A_w x^w y^. Basic properties # W(C;0,1) = A_=1 # W(C;1,1) = \sum_^A_=, C, # W(C;1,0) = A_= 1 \mbox (1,\ldots,1)\in C\ \mbox 0 \mbox # W(C;1,-1) = \sum_^A_(-1)^ = A_+(-1)^A_+\ldots+(-1)^A_+(-1)^A_ MacWilliams identity Denote the dual code of C \subset \mathbb_2^n by :C^\perp = \ (where \langle\ ,\ \rangle denotes the vector dot product and which is taken over \mathbb_2). The MacWilliams identity states that :W(C^\perp;x,y) = \frac W(C;y-x,y+x). The identity is named after Jessie MacWilliams. Distance enumerator The distance distribution or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Plane
In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect in a single point, but there are some pairs of lines (namely, parallel lines) that do not intersect. A projective plane can be thought of as an ordinary plane equipped with additional "points at infinity" where parallel lines intersect. Thus ''any'' two distinct lines in a projective plane intersect at exactly one point. Renaissance artists, in developing the techniques of drawing in perspective, laid the groundwork for this mathematical topic. The archetypical example is the real projective plane, also known as the extended Euclidean plane. This example, in slightly different guises, is important in algebraic geometry, topology and projective geometry where it may be denoted variously by , RP2, or P2(R), among other notations. There are many other projective planes, both infinite, such as the complex projective pla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coding Theory
Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage. Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods. This typically involves the removal of redundancy and the correction or detection of errors in the transmitted data. There are four types of coding: # Data compression (or ''source coding'') # Error control (or ''channel coding'') # Cryptographic coding # Line coding Data compression attempts to remove unwanted redundancy from the data from a source in order to transmit it more efficiently. For example, ZIP data compression makes data files smaller, for purposes such as to reduce Internet traffic. Data compressio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CRC Concise Encyclopedia Of Mathematics
''CRC Concise Encyclopedia of Mathematics'' is a bestselling book by American author Eric W. Weisstein. Summary The book is presented in a dictionary format. The book is divided into headwords. The book also provides relevant diagrams and illustrations. Lawsuits The book became the subject of a lawsuit between CRC Press and Eric W. Weisstein. The CRC Press claimed Weisstein's website ''MathWorld'' violated the copyright on the CRC Concise Encyclopedia of Mathematics. During the dispute, a court order shut down ''MathWorld'' for over a year starting October 23, 2000. According to Eric Weisstein's personal site, he restarted MathWorld on November 6, 2001. Wolfram Research, Stephen Wolfram, and Eric Weisstein settled with the CRC Press for an undisclosed financial award and several benefits. Among these benefits are the legal rights to reproduce ''MathWorld'' in book format again. Reception The book has consistently received good reviews. Editions * 1st edition, CRC Press, 19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
