Results 261 to 270 of about 17,873 (292)

Longest run of equal parts in a random integer composition

Discrete Mathematics, 2015
15 pages, 3 ...
Ayla Gafni
exaly   +3 more sources

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Compositions of Positive Integers

The Mathematics Teacher, 1991
During the summer of 1988, the first author conducted an institute on discrete mathematics for sixteen New Mexico high school teachers. One of the presented topics, compositions of integers, proved to be a fruitful source of interesting problems.
Richard M. Grassl, Karen Anne Johnson, Rachel Vickrey   +2 more
openaire   +1 more source

Some Inplace Identities for Integer Compositions

Quaestiones Mathematicae, 2015
In this paper, we give two new identities for compositions, or ordered partitions, of integers. These two identities are based on closely-related integer partition functions which have recently been studied. Thanks to the structure inherent in integer compositions, we are also able to extensively generalize both of these identities.
Munagi, A.O., Sellers, J.A.
openaire   +2 more sources

On the compositions of an integer

1980
We prove that for all positive integers n, the number of compositions of n in which the largest part is m is a unimodal function of m.
A. Odlyzko, B. Richmond
openaire   +1 more source

Counting staircases in integer compositions

Online Journal of Analytic Combinatorics, 2016
The main theorem establishes the generating function \(F\) which counts the number of times the staircase \(1 + 2 + 3 + \cdots + m^+\) fits inside an integer composition of \(n\). \[ F = \frac{k_m - \frac{q x^m y}{1-x} k_{m-1}}{(1-q)x^{\binom{m+1}{2}} \left( \frac{y}{1-x} \right)^m + \frac{1-x-xy}{1-x} \left( k_m - \frac{q x^m y}{1-x} k_{m-1} \right)}.
Blecher, Aubrey, Mansour, Toufik
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On cyclic compositions of positive integers

Aequationes mathematicae, 2011
Say that two compositions of n into k parts are related if they differ only by a cyclic shift. This defines an equivalence relation on the set of such compositions. Let \({\left\langle \begin{array}{c}n \\ k\end{array} \right\rangle}\) denote the number of distinct corresponding equivalence classes, that is, the number of cyclic compositions of n into ...
Arnold Knopfmacher, Florian Luca, Neville Robbins   +2 more
openaire   +1 more source

The water capacity of integer compositions

Online Journal of Analytic Combinatorics, 2018
We introduce the notion of capacity (ability to contain water) for compositions. Initially the compositions are  defined on a finite alphabet \([k]\) and thereafter on \(\mathbb{N}\). We find a capacity generating function for all compositions, the average capacity generating function and an asymptotic expression for the average capacity as the size of
Blecher, Aubrey, Brennan, Charlotte, Knopfmacher, Arnold   +2 more
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Trees with flowers: a catalog of integer partition and integer composition trees with their asymptotic analysis

Boletin De La Sociedad Matematica Mexicana
We present families of combinatorial classes described as trees with nodes that can carry one of two types of "flowers": integer partitions or integer compositions. Two parameters on the flowers of trees will be considered: the number of "petals" in all the flowers (petals' weight) and the number of edges in the petals of all the flowers (flowers ...
Yongjian Yang
exaly   +4 more sources

ON THE MEAN VALUE OF THE INDEX OF COMPOSITION OF AN INTEGER II

International Journal of Number Theory, 2012
For each integer n ≥ 2, let [Formula: see text] be the index of composition of n, where γ(n) ≔ ∏p∣np. The index of composition of an integer measures the multiplicity of its prime factors. In this paper, we obtain a new asymptotic formula of the sum ∑n≤xλ-k(n). Furthermore, we improve the error term under the Riemann Hypothesis.
Zhang, Deyu, Lü, Meimei, Zhai, Wenguang
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Irreducibility Results for Compositions of Polynomials with Integer Coefficients

Monatshefte für Mathematik, 2006
The paper begins by a very interesting survey of results on irreducibility of composite polynomials. In this work, the authors obtain explicit upper bounds for the number of irreducible factors for a class of polynomials of the form \(f \circ g\), where \(f\) and \(g\) are polynomials with integer coefficients, in terms of the degrees of \(f\) and \(g\)
Bonciocat, Anca Iuliana, Zaharescu, Alexandru   +1 more
openaire   +2 more sources