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Subtraction Game
In combinatorial game theory, a subtraction game is an abstract strategy game whose state can be represented by a natural number or vector of numbers (for instance, the numbers of game tokens in piles of tokens, or the positions of pieces on board) and in which the allowed moves reduce these numbers., "Subtraction games", pp. 83–86. Often, the moves of the game allow any number to be reduced by subtracting a value from a specified ''subtraction set'', and different subtraction games vary in their subtraction sets. These games also vary in whether the last player to move wins (the normal play convention) or loses (misère play convention). Another winning convention that has also been used is that a player who moves to a position with all numbers zero wins, but that any other position with no moves possible is a draw. Examples Examples of notable subtraction games include the following: * Nim is a game whose state consists of multiple piles of tokens, such as coins or matchsticks, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Game Theory
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Study has been largely confined to two-player games that have a ''position'' that the players take turns changing in defined ways or ''moves'' to achieve a defined winning condition. Combinatorial game theory has not traditionally studied games of chance or those that use imperfect or incomplete information, favoring games that offer perfect information in which the state of the game and the set of available moves is always known by both players. However, as mathematical techniques advance, the types of game that can be mathematically analyzed expands, thus the boundaries of the field are ever changing. Scholars will generally define what they mean by a "game" at the beginning of a paper, and these definitions often vary as they are specific to the game being analyzed and are not meant to represent the entire scope of the field. C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Golden Ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0, where the Greek letter phi ( or \phi) denotes the golden ratio. The constant \varphi satisfies the quadratic equation \varphi^2 = \varphi + 1 and is an irrational number with a value of The golden ratio was called the extreme and mean ratio by Euclid, and the divine proportion by Luca Pacioli, and also goes by several other names. Mathematicians have studied the golden ratio's properties since antiquity. It is the ratio of a regular pentagon's diagonal to its side and thus appears in the construction of the dodecahedron and icosahedron. A golden rectangle—that is, a rectangle with an aspect ratio of \varphi—may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has been used to analyze the proportions of natural object ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Journal Of Combinatorics
The ''Electronic Journal of Combinatorics'' is a peer-reviewed open access scientific journal covering research in combinatorial mathematics. The journal was established in 1994 by Herbert Wilf (University of Pennsylvania) and Neil Calkin (Georgia Institute of Technology). The Electronic Journal of Combinatorics is a founding member of the Free Journal Network. According to the ''Journal Citation Reports'', the journal had a 2017 impact factor of 0.762. Editors-in-chief Current The current editors-in-chief are: * Maria Axenovich, Karlsruhe Institute of Technology, Germany * Miklós Bóna, University of Florida, United States * Julia Böttcher, London School of Economics, United Kingdom * Richard A. Brualdi, University of Wisconsin, Madison, United States * Eric Fusy, CNRS/LIX, École Polytechnique, France * Catherine Greenhill, UNSW Sydney, Australia * Brendan McKay, Australian National University, Australia * Bojan Mohar, Simon Fraser University, Canada * Marc Noy, Universitat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Integer Sequences
The ''Journal of Integer Sequences'' is a peer-reviewed open-access academic journal in mathematics, specializing in research papers about integer sequences. It was founded in 1998 by Neil Sloane. Sloane had previously published two books on integer sequences, and in 1996 he founded the On-Line Encyclopedia of Integer Sequences (OEIS). Needing an outlet for research papers concerning the sequences he was collecting in the OEIS, he founded the journal. Since 2002 the journal has been hosted by the David R. Cheriton School of Computer Science at the University of Waterloo, with Waterloo professor Jeffrey Shallit as its editor-in-chief. There are no page charges for authors, and all papers are free to all readers. The journal publishes approximately 50–75 papers annually.. In most years from 1999 to 2014, SCImago Journal Rank has ranked the ''Journal of Integer Sequences'' as a third-quartile journal in discrete mathematics and combinatorics. It is indexed by ''Mathematical Revie ... [...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, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scripta Mathematica
''Scripta Mathematica'' was a quarterly journal published by Yeshiva University devoted to the philosophy, history, and expository treatment of mathematics. It was said to be, at its time, "the only mathematical magazine in the world edited by specialists for laymen.". The journal was established in 1932 under the editorship of Jekuthiel Ginsburg, a professor of mathematics at Yeshiva University, and its first issue appeared in 1933 at a subscription price of three dollars per year. It ceased publication in 1973. Notable papers published in ''Scripta Mathematica'' included work by Nobelist Percy Williams Bridgman concerning the implications for physics of set-theoretic paradoxes, and Hermann Weyl's obituary of Emmy Noether Amalie Emmy NoetherEmmy is the ''Rufname'', the second of two official given names, intended for daily use. Cf. for example the résumé submitted by Noether to Erlangen University in 1907 (Erlangen University archive, ''Promotionsakt Emmy Noethe .... Some s ... [...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''. The n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Computer Science (journal)
''Theoretical Computer Science'' (TCS) is a computer science journal published by Elsevier, started in 1975 and covering theoretical computer science. The journal publishes 52 issues a year. It is abstracted and indexed by Scopus and the Science Citation Index. According to the Journal Citation Reports, its 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... is 0.827. References Computer science journals Elsevier academic journals Publications established in 1975 {{comp-sci-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octal Game
The octal games are a class of two-player games that involve removing tokens (game pieces or stones) from heaps of tokens. They have been studied in combinatorial game theory as a generalization of Nim, Kayles, and similar games. Revised and reprinted as Octal games are impartial meaning that every move available to one player is also available to the other player. They differ from each other in the numbers of tokens that may be removed in a single move, and (depending on this number) whether it is allowed to remove an entire heap, reduce the size of a heap, or split a heap into two heaps. These rule variations may be described compactly by a coding system using octal numerals. Game specification An octal game is played with tokens divided into heaps. Two players take turns moving until no moves are possible. Every move consists of selecting just one of the heaps, and either * removing all of the tokens in the heap, leaving no heap, * removing some but not all of the tokens, le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grundy's Game
Grundy's game is a two-player mathematical game of strategy. The starting configuration is a single heap of objects, and the two players take turn splitting a single heap into two heaps of different sizes. The game ends when only heaps of size two and smaller remain, none of which can be split unequally. The game is usually played as a '' normal play'' game, which means that the last person who can make an allowed move wins. Illustration A normal play game starting with a single heap of 8 is a win for the first player provided they start by splitting the heap into heaps of 7 and 1: player 1: 8 → 7+1 Player 2 now has three choices: splitting the 7-heap into 6 + 1, 5 + 2, or 4 + 3. In each of these cases, player 1 can ensure that on the next move he hands back to his opponent a heap of size 4 plus heaps of size 2 and smaller: player 2: 7+1 → 6+1+1 player 2: 7+1 → 5+2+1 player 2: 7+1 → 4+3+1 player 1: 6+1+1 → 4+2+1+1 player 1: 5+2+1 → 4+1+2+1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Undecidable Problem
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer. The halting problem is an example: it can be proven that there is no algorithm that correctly determines whether arbitrary programs eventually halt when run. Background A decision problem is any arbitrary yes-or-no question on an infinite set of inputs. Because of this, it is traditional to define the decision problem equivalently as the set of inputs for which the problem returns ''yes''. These inputs can be natural numbers, but also other values of some other kind, such as strings of a formal language. Using some encoding, such as a Gödel numbering, the strings can be encoded as natural numbers. Thus, a decision problem informally phrased in terms of a formal language is also equivalent to a set of natural numbers. To keep the formal definition simple, it is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas S
Thomas may refer to: People * List of people with given name Thomas * Thomas (name) * Thomas (surname) * Saint Thomas (other) * Thomas Aquinas (1225–1274) Italian Dominican friar, philosopher, and Doctor of the Church * Thomas the Apostle * Thomas (bishop of the East Angles) (fl. 640s–650s), medieval Bishop of the East Angles * Thomas (Archdeacon of Barnstaple) (fl. 1203), Archdeacon of Barnstaple * Thomas, Count of Perche (1195–1217), Count of Perche * Thomas (bishop of Finland) (1248), first known Bishop of Finland * Thomas, Earl of Mar (1330–1377), 14th-century Earl, Aberdeen, Scotland Geography Places in the United States * Thomas, Illinois * Thomas, Indiana * Thomas, Oklahoma * Thomas, Oregon * Thomas, South Dakota * Thomas, Virginia * Thomas, Washington * Thomas, West Virginia * Thomas County (other) * Thomas Township (other) Elsewhere * Thomas Glacier (Greenland) Arts, entertainment, and media * ''Thomas'' (Burton novel) 1969 novel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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