Results 301 to 310 of about 863,417 (323)

The “best” partition of an integer

BIT, 1974
An algorithm, based on a conjecture, to compute a permutation whose repeated application to a given set will yield a maximum number of different orderings of that set is presented. The algorithm gives the lengths of the cycles required. This problem turns out to be equivalent to the problem of determining a partitionB(n) ofn for which the least common ...
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Notes on integer partitions

International Journal of Approximate Reasoning, 2022
Abstract Some observations concerning the lattices of integer partitions are presented. We determine the size of the standard contexts, discuss a recursive construction and show that the lattices have unbounded breadth.
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Two Self-Dual Lattices of Signed Integer Partitions

, 2014
In this paper we study two self-dual lattices of signed integer partitions, D(m, n) and E(m, n), which can be considered also sub-lattices of the lattice L(m, 2n), where L(m, n) is the lattice of all the usual integer partitions with at most m parts and ...
G. Chiaselotti, W. Keith, P. Oliverio
semanticscholar   +1 more source

Multistage Robust Mixed-Integer Optimization with Adaptive Partitions

Operational Research, 2016
We present a new partition-and-bound method for multistage adaptive mixed-integer optimization (AMIO) problems that extends previous work on finite adaptability.
D. Bertsimas, Iain Dunning
semanticscholar   +1 more source

Sampling part sizes of random integer partitions

, 2013
Let $$\lambda $$λ be a partition of the positive integer $$n$$n, selected uniformly at random among all such partitions. Corteel et al. (Random Stuct Algorithm 14:185–197, 1999) proposed three different procedures of sampling parts of $$\lambda $$λ at ...
L. Mutafchiev
semanticscholar   +1 more source

Successions in integer partitions

The Ramanujan Journal, 2008
A partition of an integer n is a representation n=a1+a2+⋅⋅⋅+ak, with integer parts 1≤a1≤a2≤…≤ak. For any fixed positive integer p, a p-succession in a partition is defined to be a pair of adjacent parts such that ai+1−ai=p. We find generating functions for the number of partitions of n with no p-successions, as well as for the total number of such ...
Augustine O. Munagi, Arnold Knopfmacher
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Multi-lump wave patterns of KPI via integer partitions

Physica A: Statistical Mechanics and its Applications, 2023
S. Chakravarty, Michael Zowada
semanticscholar   +1 more source

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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Partitions of positive integers

International Journal of Mathematical Education in Science and Technology, 1994
Because 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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Integer partitions into Diophantine pairs

Quaestiones Mathematicae, 2017
Let 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 ...
N. Benyahia-Tani, Farid Bencherif, Z. Yahi, S. Bouroubi, Omar Kihel   +4 more
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