Results 261 to 270 of about 46,123 (300)

On an Identity with Binomial Coefficients

Mathematical Notes, 2019
In the present paper, a new identity associated with binomial coefficients is considered. This identity generates linear forms in the values of consecutive zeta constants generalizing the number-theoretic Apery-Beukers approach, which gives a chance to acquire novel algorithms for effectively evaluating of the Riemann zeta function at the integer ...
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Fast computation of binomial coefficients

Numerical Algorithms, 2020
One problem that arises in computation involving large numbers is precision. In certain situations, the result might be represented by the standard data type, but arithmetic precision might be compromised when dealing with large numbers in the course to the result. Binomial coefficients are an example that suffer from this torment. In the present paper,
Leonardo Carneiro de Araújo, João Pedro H. Sansão, Adriano S. Vale-Cardoso   +2 more
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On the scarcity of powerful binomial coefficients

Mathematika, 1999
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A Regular Determinant of Binomial Coefficients

Proceedings of the American Mathematical Society, 1973
Let n be a positive integer and suppose that each of {a,}' and (c,)} is an increasing sequence of nonnegative integers. Let M be the n x n matrix such that M ij=C(a,, Cj), where C(m, n) is the number of combinations of m objects taken n at a time. We give an explicit formula for the determinant of M as a sum of nonnegative quantities. Further, if ai>cj,
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The Binomial Coefficient

2015
We now turn our attention to one of the most fundamental and useful notions in all of combinatorics, the binomial coefficient. You may recall the binomial coefficient from high-school algebra class. However, we will give several other interpretations for this concept.
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Binomial coefficient computation

ACM SIGCSE Bulletin, 2002
Binomial coefficient computation, i.e. the calculation of the number of combinations of n objects taken k at a time, C(n,k), can be performed either by using recursion or by iteration. Here, we elaborate on a previous report [6], which presented recursive methods on binomial coefficient calculation and propose alternative efficient iterative methods ...
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Binomial Coefficients, Valuations, and Words

2017
The study of arithmetic properties of binomial coefficients has a rich history. A recurring theme is that p-adic statistics reflect the base-p representations of integers. We discuss many results expressing the number of binomial coefficients \(\left( {\begin{array}{c}n\\ m\end{array}}\right) \) with a given p-adic valuation in terms of the number of ...
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Generalized alternating hyperharmonic number sums with reciprocal binomial coefficients

Journal of Mathematical Analysis and Applications, 2021
Ruşen Li
exaly  

On the divisibility of sums of even powers of q-binomial coefficients

Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2022
Ji-Cai Liu, Xue-Ting Jiang
exaly  

Note on the Binomial Coefficients

Journal of the London Mathematical Society, 1948
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