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Integer partitions into Diophantine pairs
Quaestiones Mathematicae, 2017Let n, a and b be positive integers. The pair (a; b) is called an integer partition of n into Diophantine pair if n = a+b, ab+1 is a perfect square and a > b. In this paper we give, for any positive integer n, a closed formula for the number of integer partitions into Diophantine pairs.Mathematics Subject Classication (2010): Primary 05A17 ...
Bencherif, F. +4 more
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On Product Partitions of Integers
Canadian Mathematical Bulletin, 1991AbstractLet p*(n) denote the number of product partitions, that is, the number of ways of expressing a natural number n > 1 as the product of positive integers ≥ 2, the order of the factors in the product being irrelevant, with p*(1) = 1. For any integer if d is an ith power, and = 1, otherwise, and let . Using a suitable generating function for p*(
Harris, V. C., Subbarao, M. V.
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Constrained Integer Partitions
2004We consider the problem of partitioning n integers into two subsets of given cardinalities such that the discrepancy, the absolute value of the difference of their sums, is minimized. The integers are i.i.d. random variables chosen uniformly from the set {1,...,M}. We study how the typical behavior of the optimal partition depends on n,M and the bias s,
Christian Borgs +3 more
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Successions in integer partitions
The Ramanujan Journal, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Knopfmacher, Arnold +1 more
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Distinct r-tuples in integer partitions
The Ramanujan Journal, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Margaret Archibald +2 more
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A New Approach to Integer Partitions
Bulletin of the Brazilian Mathematical Society, New Series, 2018The two-line matrix representing integer partitions was first introduced by Frobenius more than a century ago. This paper deals with a new approach to these matrix representations considering the lattice paths induced by the two-line matrix representations. Each path is associated to a partition of another integer, which turns out to have only distinct
J. P. O. Santos, M. L. Matte
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1974
The concept of partition of integers belongs to number theory as well as to combinatorial analysis. This theory was established at the end of the 18-th century by Euler. (A detailed account of the results up to ca. 1900 is found in [*Dickson, II, 1919], pp. 101–64.) Its importance was enhanced by [Hardy, Ramanujan, 1918] and [Rademacher, 1937a, b, 1938,
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The concept of partition of integers belongs to number theory as well as to combinatorial analysis. This theory was established at the end of the 18-th century by Euler. (A detailed account of the results up to ca. 1900 is found in [*Dickson, II, 1919], pp. 101–64.) Its importance was enhanced by [Hardy, Ramanujan, 1918] and [Rademacher, 1937a, b, 1938,
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Partitions of positive integers
International Journal of Mathematical Education in Science and Technology, 1994Because they exhibit so many beautiful and intriguing relations, numbers are an inexhaustible source of fascination. This paper will show how to answer a variety of questions about partitions of a positive integer n using three easily constructed tables, and give a particularly simple and efficient way to calculate the number of partitions of large n ...
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Casting Light on Integer Partitions
Summary: Integer partitions ofnare viewed as bargraphs (i.e., Young diagrams rotated anticlockwise by 90 degrees) in which theith part of the partition \(x_i\) is given by the \(i\)th column of the bargraph with \(x_i\) cells. The sun is at infinity in the northwest of our two dimensional model and each cell may or may not be lit depending on whether ...Blecher, Aubrey +2 more
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Integer programming by partitioning
ACM SIGMAP Bulletin, 1973Integer Programming problems can be solved by a variety of methods. These can be grouped as follows:Complete EnumerationImplicit EnumerationBranch and BoundCutting PlanesPartitioningAsymptotic (or Group) TheoryConvex Analysis.The first two were discussed in educational series #2. This paper discusses the partitioning approach.
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