Results 181 to 190 of about 144,275 (215)
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2007
We present several results concerning the number of positions and games of Go. We derive recurrences for L(m, n), the number of legal positions on an m × n board, and develop a dynamic programming algorithm which computes L(m, n) in time O(m3n2λm) and space O(mλm), for some constant λ < 5.4. An implementation of this algorithm enables us to list L(n, n)
John Tromp, Gunnar Farnebäck
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We present several results concerning the number of positions and games of Go. We derive recurrences for L(m, n), the number of legal positions on an m × n board, and develop a dynamic programming algorithm which computes L(m, n) in time O(m3n2λm) and space O(mλm), for some constant λ < 5.4. An implementation of this algorithm enables us to list L(n, n)
John Tromp, Gunnar Farnebäck
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Research on Language and Computation, 2003
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The Combinatorics of Differentiation
2008Let S 1 , S 2 , ... be a sequence of finite sets, and suppose we are asked to find the sequence of cardinalities s[1], s[2], .... We are usually satisfied to find a closed-form expression for the a-generating function $F_S(z) = \sum_{n \geq 0} s[n]a[n] { z^n}$, where a[n] is a fixed positive causal sequence.
Bertiger, Anna S. +2 more
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2009
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and ...
Philippe Flajolet, Robert Sedgewick
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Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and ...
Philippe Flajolet, Robert Sedgewick
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2006
Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory.
Terence Tao, Van H. Vu
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Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory.
Terence Tao, Van H. Vu
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Studia Logica, 1988
This interesting paper is mostly concerned with Ramsey type theorems, where a theorem is of this type if it takes the form ``if certain sets are partitioned, then at least one of these parts has some particular property.'' Since a standard partition is usually considered to be a finite collection, then nonstandard methods should be of considerable ...
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This interesting paper is mostly concerned with Ramsey type theorems, where a theorem is of this type if it takes the form ``if certain sets are partitioned, then at least one of these parts has some particular property.'' Since a standard partition is usually considered to be a finite collection, then nonstandard methods should be of considerable ...
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2004
Set is a fundamental, abstract notion. A set is defined as a collection of objects, which are called the elements or points of the set. The notions of union (A ∪ B, where A and B are each sets), intersection (A ∩ B) and complement (A c ) correspond to everyday usage.
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Set is a fundamental, abstract notion. A set is defined as a collection of objects, which are called the elements or points of the set. The notions of union (A ∪ B, where A and B are each sets), intersection (A ∩ B) and complement (A c ) correspond to everyday usage.
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