Results 1  10
of
839
Binomial coefficients ()
, 2006
"... ABSTRACT. The sequence n ↦ → () a n of real binomial coefficients is studied in two main cases: a ≫ n and n ≫ a. In the first case a uniform approximation with high accuracy is obtained, in contrast to DeMoivreLaplace approximation, which has essentially local character and is good only for n ≈ a ..."
Abstract
 Add to MetaCart
ABSTRACT. The sequence n ↦ → () a n of real binomial coefficients is studied in two main cases: a ≫ n and n ≫ a. In the first case a uniform approximation with high accuracy is obtained, in contrast to DeMoivreLaplace approximation, which has essentially local character and is good only for n ≈ a
Binomial coefficients ()
, 2006
"... Abstract. We prove that if the signed binomial coefficient (−1) i`k ´ viewed i modulo p is a periodic function of i with period h in the range 0 ≤ i ≤ k, then k + 1 is a power of p, provided h is prime to p and not too large compared to k. (In particular, 2h ≤ k suffices.) As an application, we prov ..."
Abstract
 Add to MetaCart
Abstract. We prove that if the signed binomial coefficient (−1) i`k ´ viewed i modulo p is a periodic function of i with period h in the range 0 ≤ i ≤ k, then k + 1 is a power of p, provided h is prime to p and not too large compared to k. (In particular, 2h ≤ k suffices.) As an application, we
Integral Representations and Binomial Coefficients
"... In this article, we present two extensions of Sofo’s theorems on integral representations of ratios of reciprocals of double binomial coefficients. From the two extensions, we get several new relations between integral representations and binomial coefficients. 1 ..."
Abstract
 Add to MetaCart
In this article, we present two extensions of Sofo’s theorems on integral representations of ratios of reciprocals of double binomial coefficients. From the two extensions, we get several new relations between integral representations and binomial coefficients. 1
TWO BINOMIAL COEFFICIENT CONJECTURES
"... Abstract. Much is known about binomial coefficients where primes are concerned, but considerably less is known regarding prime powers and composites. This paper provides two conjectures in these directions, one about counting binomial coefficients modulo 16 and one about the value of ( n ..."
Abstract
 Add to MetaCart
Abstract. Much is known about binomial coefficients where primes are concerned, but considerably less is known regarding prime powers and composites. This paper provides two conjectures in these directions, one about counting binomial coefficients modulo 16 and one about the value of ( n
ON DIVISIBILITY OF BINOMIAL COEFFICIENTS
 J. AUSTRAL. MATH. SOC. 93(2012), NO. 12, 189–201.
, 2012
"... In memory of Prof. Alf van der Poorten Abstract. Motivated by Catalan numbers and higherorder Catalan numbers, we study in this paper factors of products of at most two binomial coefficients. ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
In memory of Prof. Alf van der Poorten Abstract. Motivated by Catalan numbers and higherorder Catalan numbers, we study in this paper factors of products of at most two binomial coefficients.
On p, qbinomial coefficients
 Integers 8 (2008) #A29
"... Abstract In this paper, we develop the theory of a p, qanalogue of the binomial coefficients. Some properties and identities parallel to those of the usual and qbinomial coefficients will be established including the triangular, vertical, and the horizontal recurrence relations, horizontal genera ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Abstract In this paper, we develop the theory of a p, qanalogue of the binomial coefficients. Some properties and identities parallel to those of the usual and qbinomial coefficients will be established including the triangular, vertical, and the horizontal recurrence relations, horizontal
MORE BINOMIAL COEFFICIENT CONGRUENCES
, 1990
"... In 1878 Edouard Lucas gave the following result for computing binomial coefficients modulo a prime [3], [4]. Theorem 1.1: If p is a prime, n, r, n^, and rQ are nonnegative integers, and ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
In 1878 Edouard Lucas gave the following result for computing binomial coefficients modulo a prime [3], [4]. Theorem 1.1: If p is a prime, n, r, n^, and rQ are nonnegative integers, and
Planar Binomial Coefficients
, 2005
"... The notion of binomial coefficients ( T) S of finite planar, reduced rooted trees T,S is defined and a recursive formula for its computation is shown. The nonassociative binomial formula (1 + x) T = ∑ T ..."
Abstract
 Add to MetaCart
The notion of binomial coefficients ( T) S of finite planar, reduced rooted trees T,S is defined and a recursive formula for its computation is shown. The nonassociative binomial formula (1 + x) T = ∑ T
Double Sums of Binomial Coefficients
"... Abstract. We investigate the representation of double sums of binomial coefficients in integral form using the properties of the Beta function. Some nice identities result. Mathematics Subject Classification: Primary 11B65 ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. We investigate the representation of double sums of binomial coefficients in integral form using the properties of the Beta function. Some nice identities result. Mathematics Subject Classification: Primary 11B65
Functions of the Binomial Coefficient
, 2008
"... available for noncommercial, educational purposes, provided that this copyright statement appears on the reproduced materials and notice is given that the copying is by permission of the author. To disseminate otherwise or to republish requires written permission from the author. The wellknown bi ..."
Abstract
 Add to MetaCart
known binomial coefficient is the building block of Pascal’s triangle. We explore the relationship between functions of the binomial coefficient and Pascal’s triangle, providing proofs of connections between Catalan numbers, determinants, nonintersecting paths, and Baxter permutations. Contents Abstract iii
Results 1  10
of
839