Results 21 to 30 of about 46,762 (263)
On Binomial Coefficient Residues [PDF]
Canadian Journal of Mathematics, 1957 The number of binomial coefficients , which are congruent to j , 0 ≤ j ≤ p − 1, modulo the prime number p is denoted by θj(n). In this paper we give systems of simultaneous linear difference equations with constant coefficients whose
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Poset binomials and rainbow characters [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 This paper introduces a variation on the binomial coefficient that depends on a poset and interpolates between $q$-binomials and 1-binomials: a total order gives the usual $q$-binomial, and a poset with no relations gives the usual binomial coefficient ...
Daniel Bragg, Nathaniel Thiem
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ON DIVISIBILITY OF BINOMIAL COEFFICIENTS [PDF]
Journal of the Australian Mathematical Society, 2012 AbstractIn this paper, motivated by Catalan numbers and higher-order Catalan numbers, we study factors of products of at most two binomial coefficients.
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Ray trajectories, binomial coefficients of a new type, and the binary system [PDF]
Компьютерные исследования и моделирование, 2010 The paper describes a new algorithm of construction of the nonlinear arithmetic triangle on the basis of numerical simulation and the binary system. It demonstrates that the numbers that fill the nonlinear arithmetic triangle may be binomial coefficients
Aleksandr Vladimirovich Yurkin
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Plane Partitions and a Problem of Josephus
Mathematics, 2023 The Josephus Problem is a mathematical counting-out problem with a grim description: given a group of n persons arranged in a circle under the edict that every kth person will be executed going around the circle until only one remains, find the position ...
Mircea Merca
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A generalization of the binomial coefficients
Discrete Mathematics, 1992 We pose the question of what is the best generalization of the factorial and the binomial coefficient. We give several examples, derive their combinatorial properties, and demonstrate their interrelationships. On cherche ici à déterminer est la meilleure généralisation possible des factorielles et des coefficients du binôome. On s'interesse à plusieurs
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A $q$-analog of Ljunggren's binomial congruence [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We prove a $q$-analog of a classical binomial congruence due to Ljunggren which states that $\binom{ap}{bp} \equiv \binom{a}{b}$ modulo $p^3$ for primes $p \geq 5$.
Armin Straub
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Inequalities for Binomial Coefficients
Journal of Mathematical Analysis and Applications, 1999 For any real number \(r\) with \(r>1\), let \(c_r= (2\pi(1-{1\over r}))^{-1/2}\) and \(d_r= (r-1)/(1-{1\over r})^r\). Let \(B_{2m}\) \((m= 1,2,\dots)\) be the Bernoulli numbers defined by \[ {z\over e^z-1}=1-{z\over 2}+\sum^\infty_{m=1} B_{2m}{z^{2m}\over (2m)!}.
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The update exposition of the components organising the sum of weighted equal powers
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2012 The sum of the weighted equal powers with natural bases and parameters is organized of components, which are independent or dependent on weight coefficients.
A. I. Nikonov
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