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Factors of Binomial Coefficients
The Mathematical Gazette, 1959If Pascal’s Triangle is written down, it will be noticed that the number of odd numbers in any row is a power of 2; moreover, if every even number is replaced by 0 and every odd number by 1, the result is an interesting pattern of triangles from which it is possible to deduce a general rule.
Lockwood, E. H., Gant, P.
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On the Conditioned Binomial Coefficients
Integers, 2011AbstractWe answer a question on the conditioned binomial coefficients raised in an article of Barlotti and Pannone, thus giving an alternative proof of an extension of Frobenius' generalization of Sylow's theorem.
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On an Identity with Binomial Coefficients
Mathematical Notes, 2019In 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, 2020One 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 +2 more
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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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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, 2002Binomial 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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On the scarcity of powerful binomial coefficients
Mathematika, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Regular Determinant of Binomial Coefficients
Proceedings of the American Mathematical Society, 1973Let 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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