Results 11 to 20 of about 1,803 (199)
Elementary proofs in the theory of partitions
Mathematische Zeitschrift, 1963 Let \(k>1\) be an integer, and let \(a_1, a_2, \ldots, a_s\) be \(s\) distinct positive integers not exceeding \(k\). The set of nonnegative integers \(\nu\) such that \(\nu\equiv a_i \pmod k\) for some \(i\), \(1\leq i\leq s\) is called a congruence set modulo \(k\), and is denoted by \(a\). Let \(F(x; a)= \prod_{\nu\in a} (1-x^\nu)^{-1} = \sum p_n(a)
E. Grosswald
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Modularity, balance, and frustration in student social networks: The role of negative relationships in communities. [PDF]
PLoS ONE, 2022 Signed networks provide information to study the structure and composition of relationships (positive and negative) among individuals in a complex system. Individuals, through different criteria, form groups or organizations called communities. Community
José Brito-Montes +2 more
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Counting certain quadratic partitions of zero modulo a prime number
Open Mathematics, 2021 Consider an odd prime number p≡2(mod3)p\equiv 2\hspace{0.3em}\left(\mathrm{mod}\hspace{0.3em}3). In this paper, the number of certain type of partitions of zero in Z/pZ{\mathbb{Z}}\hspace{-0.1em}\text{/}\hspace{-0.1em}p{\mathbb{Z}} is calculated using a ...
Xiao Wang, Li Aihua
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Rational Numbers under the interpretation of measurement: a study using Frac-Soma
Revista de Ensino de Ciências e MatemáticaThis article addresses the learning of rational numbers, focusing on their measured interpretation and the use of Frac-Soma as a trigger for both figural and numerical representations, based on activities developed with 7th-grade elementary school ...
Claudia Aparecida Winkelmann +2 more
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Arithmetic properties of k-tuple ℓ-regular partitions [PDF]
Journal of Mathematical Analysis and ApplicationsIn this paper, we study arithmetic properties satisfied by the $k$-tuple $\ell$-regular partitions. A $k$-tuple of partitions $(\xi_1, \xi_2, \ldots, \xi_k)$ is said to be $\ell$-regular if all the $\xi_i$'s are $\ell$-regular. We study the cases $(\ell,
Manjil Saikia, Abhishek Sarma
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An elementary solution to a problem in restricted partitions
Journal of Combinatorial Theory, 1970 N. Metropolis, P. Stein
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Homogeneous Banach Spaces as Banach Convolution Modules over M(G)
Mathematics, 2022 This paper is supposed to form a keystone towards a new and alternative approach to Fourier analysis over LCA (locally compact Abelian) groups G.
Hans Georg Feichtinger
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Real-world applications of number theory [PDF]
ریاضی و جامعهThe above abstract has been extracted by the translator from the original article (J. Klaška, Real-world applications of number theory, South Bohemia Mathematical Letters, 25 no.
Rahim Rahmati-Asghar
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Hypersymmetric functions and Pochhammers of 2×2 nonautonomous matrices
International Journal of Mathematics and Mathematical Sciences, 2004 We introduce the hypersymmetric functions of 2×2 nonautonomous matrices and show that they are related, by simple expressions, to the Pochhammers (factorial polynomials) of these matrices.
A. F. Antippa
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ELEMENTARY PROOFS OF PARITY RESULTS FOR 5-REGULAR PARTITIONS
Bulletin of the Australian Mathematical Society, 2009 In a recent paper, Calkin et al. [N. Calkin, N. Drake, K. James, S. Law, P. Lee, D. Penniston and J. Radder, ‘Divisibility properties of the 5-regular and 13-regular partition functions’, Integers8 (2008), #A60] used the theory of modular forms to ...
M. Hirschhorn, James A. Sellers
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