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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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Binomial coefficient recursion
ACM SIGCSE Bulletin, 2001The binomial coefficient or, alternatively, the number of combinations of n items taken k at a time, provides two defining recurrences. One of these provides a very useful recursive function a very good way for a program to calculate this function. The other provides a
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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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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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2007
In this paper, we develop the theory of a p, q-analogue of the binomial coefficients. Some properties and identities parallel to those of the usual and q-binomial coefficients will be established including the triangular, vertical, and the horizontal recurrence relations, horizontal generating function, and the orthogonality and inverse relations.
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In this paper, we develop the theory of a p, q-analogue of the binomial coefficients. Some properties and identities parallel to those of the usual and q-binomial coefficients will be established including the triangular, vertical, and the horizontal recurrence relations, horizontal generating function, and the orthogonality and inverse relations.
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Equal Binomial Coefficients [PDF]
, 1995 We give a conjecture on the set of numbers that occurs at least 6 times in the Pascal Triangle. We determine all the integral and some rational solutions of the special case n choose 3 = m choose 4.
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