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On Intersecting Properties of Partitions of Integers
Combinatorics, Probability and Computing, 2005We derive a generalization of a theorem of Raimi proving there is a partition of natural numbers with given densities of classes which meet structured translates of any other class of a partition of natural numbers.
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2004
The theory of integer partitions is a subject of enduring interest. A major research area in its own right, it has found numerous applications, and celebrated results such as the Rogers-Ramanujan identities make it a topic filled with the true romance of mathematics.
George E. Andrews, Kimmo Eriksson
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The theory of integer partitions is a subject of enduring interest. A major research area in its own right, it has found numerous applications, and celebrated results such as the Rogers-Ramanujan identities make it a topic filled with the true romance of mathematics.
George E. Andrews, Kimmo Eriksson
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An Identity for Partitions of Integers: 10809
The American Mathematical Monthly, 2002The binomial theorem and F(uj) = B1 turn the right side of (2) into the right side of the desired identity. The left side of (2) becomes the left side of the desired identity by application of (1), the substitution j = n k, and F(Un-j+h) = Bn-j+h Editorial comment.
David Beckwith, Karl David
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Cell Patterns in Integer Partitions
J. Autom. Lang. Comb., 2019A partition of a positive integer $n$ is a finite nonincreasing sequence of positive integers whose sum is $n$. Integer partitions can be graphically represented through Ferrers diagrams (graphs). These diagrams may contain smaller partitions, defined as cell patterns.
Toufik Mansour +2 more
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The minimal excludant in integer partitions
J. Integer Seq., 2020\textit{A. S. Fraenkel} and \textit{U. Peled} [Math. Sci. Res. Inst. Publ. 63, 77--94 (2015; Zbl 1405.91081)] have defined the minimal excludant or mex-function on a set \(S\) of positive integers as the least positive integer not in \(S\). The authors of this paper considered the mex-function applied to integer partitions and provide numerous ...
George E. Andrews, David Newman
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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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An Efficient Representation of Partitions of Integers
2018We introduce a data structure for representing a partition of an integer n, which uses \(\mathrm{O}(\sqrt{n})\) bits of space. This is constant multiple of the information theoretic lower bound. Three types of operations \(\mathsf{access}_\mathsf{p},\mathsf{bound}_\mathsf{p},\mathsf{prefixsum}_\mathsf{p}\) are supported in constant time by using the ...
Kentaro Sumigawa, Kunihiko Sadakane
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An improved approximation algorithm for the minimum common integer partition problem
Information and Computation, 2021Weitian Tong, Guohui Lin
exaly