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Author: George E. Andrews
Publisher: Cambridge University Press
ISBN: 9780521637664
Category : Mathematics
Languages : en
Pages : 274
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Book Description
Discusses mathematics related to partitions of numbers into sums of positive integers.
Author: William Bernard Gordon
Publisher:
ISBN:
Category :
Languages : en
Pages : 50
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Author: Darren Vincent Lee
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: George E. Andrews
Publisher: Cambridge University Press
ISBN: 9780521637664
Category : Mathematics
Languages : en
Pages : 274
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Book Description
Discusses mathematics related to partitions of numbers into sums of positive integers.
Author: Stevo Todorcevic
Publisher: American Mathematical Soc.
ISBN: 0821850911
Category : Mathematics
Languages : en
Pages : 130
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Book Description
This book presents results on the case of the Ramsey problem for the uncountable: When does a partition of a square of an uncountable set have an uncountable homogeneous set? This problem most frequently appears in areas of general topology, measure theory, and functional analysis. Building on his solution of one of the two most basic partition problems in general topology, the ``S-space problem,'' the author has unified most of the existing results on the subject and made many improvements and simplifications. The first eight sections of the book require basic knowldege of naive set theory at the level of a first year graduate or advanced undergraduate student. The book may also be of interest to the exclusively set-theoretic reader, for it provides an excellent introduction to the subject of forcing axioms of set theory, such as Martin's axiom and the Proper forcing axiom.
Author: George E. Andrews
Publisher: Cambridge University Press
ISBN: 9780521600903
Category : Mathematics
Languages : en
Pages : 156
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Book Description
Provides a wide ranging introduction to partitions, accessible to any reader familiar with polynomials and infinite series.
Author: Gabor Halasz
Publisher: Springer Science & Business Media
ISBN: 3642613241
Category : Mathematics
Languages : en
Pages : 165
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Book Description
The problem of uniform distribution of sequences initiated by Hardy, Little wood and Weyl in the 1910's has now become an important part of number theory. This is also true, in relation to combinatorics, of what is called Ramsey theory, a theory of about the same age going back to Schur. Both concern the distribution of sequences of elements in certain collection of subsets. But it was not known until quite recently that the two are closely interweaving bear ing fruits for both. At the same time other fields of mathematics, such as ergodic theory, geometry, information theory, algorithm theory etc. have also joined in. (See the survey articles: V. T. S6s: Irregularities of partitions, Lec ture Notes Series 82, London Math. Soc. , Surveys in Combinatorics, 1983, or J. Beck: Irregularities of distributions and combinatorics, Lecture Notes Series 103, London Math. Soc. , Surveys in Combinatorics, 1985. ) The meeting held at Fertod, Hungary from the 7th to 11th of July, 1986 was to emphasize this development by bringing together a few people working on different aspects of this circle of problems. Although combinatorics formed the biggest contingent (see papers 2, 3, 6, 7, 13) some number theoretic and analytic aspects (see papers 4, 10, 11, 14) generalization of both (5, 8, 9, 12) as well as irregularities of distribution in the geometric theory of numbers (1), the most important instrument in bringing about the above combination of ideas are also represented.
Author: Russell Smucker
Publisher:
ISBN:
Category : Partitions (Mathematics)
Languages : en
Pages : 96
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Author: Jaclyn Ann Anderson
Publisher:
ISBN:
Category :
Languages : en
Pages : 74
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Author: Karthik Nataraj
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Chapter 1: Partitions without sequences of consecutive integers as parts have been studied recently by many authors, including Andrews, Holroyd, Liggett, and Romik, among others. Their results include a description of combinatorial properties, hypergeometric representations for the generating functions, and asymptotic formulas for the enumeration functions. We complete a similar investigation of partitions into distinct parts without sequences, which are of particular interest due to their relationship with the Rogers-Ramanujan identities. Our main results include a double series representation for the generating function, an asymptotic formula for the enumeration function, and several combinatorial inequalities.Chapter 2: We use the idea of index invariance under the Franklin mapping to prove higher power generalizations of two results discovered by M. V. Subbarao. We then apply similar ideas to a two-variable generalization of the Rogers-Ramanujan identities due to G. E. Andrews.
Author: Paul Turán
Publisher:
ISBN:
Category : Mathematicians
Languages : en
Pages : 936
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