Results 281 to 290 of about 180,663 (331)
Some of the next articles are maybe not open access.
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.
openaire +2 more sources
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 ...
openaire +1 more source
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
openaire +1 more source
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.
openaire +1 more source
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.
openaire +1 more source
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.
openaire +1 more source
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.
openaire +2 more sources
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.
openaire +2 more sources
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.
openaire