Results 161 to 170 of about 246,865 (191)

An Identity for Partitions of Integers: 10809

The American Mathematical Monthly, 2002
The 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., 2019
A 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, Armend Shaban Shabani, Daniel Yaqubi   +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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Partitions of Integers

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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An Efficient Representation of Partitions of Integers

2018
We 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
openaire   +1 more source

Notes on integer partitions

International Journal of Approximate Reasoning, 2022
Bernhard Ganter
exaly  

Partition of Integers

ACM Transactions on Mathematical Software, 1976
openaire   +2 more sources

Integer Partition

2023
Yung-Hsiang Lu, George K. Thiruvathukal
openaire   +1 more source

Dyson's crank and the mex of integer partitions

Journal of Combinatorial Theory - Series A, 2022
Brian Hopkins, Dennis Stanton
exaly  

Fast algorithms for genegrating integer partitions

International Journal of Computer Mathematics, 1998
Ivan Stojmenovic
exaly