Results 241 to 250 of about 258,537 (280)

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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Generalizing inplace multiplicity identities for integer compositions

Quaestiones Mathematicae, 2017
AbstractIn a recent paper, the authors gave two new identities for compositions, or ordered partitions, of integers. These identities were based on closely-related integer partition functions which have recently been studied. In the process, we also extensively generalized both of these identities.
Augustine O. Munagi, James A. Sellers
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Aperiodic compositions and classical integer sequences

2017
Summary: In this paper we define the notion of singular composition of a positive integer. We provide a characterization of these compositions, together with methods for decomposing and also extending a singular composition in terms of other singular compositions.
FERRARI, MARGHERITA MARIA, Zagaglia Salvi, N.   +1 more
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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
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On the Number of Primality Witnesses of Composite Integers

Russian Mathematics, 2021
The Miller-Rabin test tries to determine the primality of a given odd number \(n\), see [\textit{M. O. Rabin}, J. Number Theory 12, 128--138 (1980; Zbl 0426.10006)].
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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
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A Unified Approach to Algorithms Generating Unrestricted and Restricted Integer Compositions and Integer Partitions

Journal of Mathematical Modelling and Algorithms, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Runs of composite integers and the Chinese Remainder Theorem

The Mathematical Gazette, 1994
The distribution of the prime numbers is of course a well-trodden path. The casual enquirer, working with small numbers, soon finds that the distribution has no obvious regularities, and sees that the primes thin out. The Prime number theorem (which is not elementary) helps to firm up this ...
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Distribution of the partition function modulo composite integers M

Mathematische Annalen, 2000
Ramanujan's partition congruences are \[ p(5n+4)\equiv 0\pmod 5, \quad p(7n+5)\equiv 0\pmod 7, \quad p(11n+6)\equiv 0\pmod {11}. \] These have extensions modulo powers of 5, 7, 11. In general, congruences of the form \[ p(An+B)\equiv 0\pmod M \] are very rare. However, \textit{K. Ono} [Ann. Math.
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Integer topological defects organize stresses driving tissue morphogenesis

Nature Materials, 2022
Pau Guillamat, Carles Blanch-Mercader, Karsten Kruse   +2 more
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