Topic
Binomial number
About: Binomial number is a research topic. Over the lifetime, 151 publications have been published within this topic receiving 1598 citations.
Papers published on a yearly basis
Papers
351 citations
Journal Article•
TL;DR: The main idea of as discussed by the authors is to consider generalized binomial coefficients that are formed from an arbitrary sequence C and isolate a property of the sequence C that guarantees the existence of a theorem like Kummer's, relating divisibility by prime powers to carries.
Abstract: The main idea is to consider generalized binomial coefficients that are formed from an arbitrary sequence C, as shown in (3) below. We will isolate a property of the sequence C that guarantees the existence of a theorem like Kummer’s, relating divisibility by prime powers to carries in addition. A special case of the theorem we shall prove describes the prime power divisibility of Gauss’s generalized binomial coefficients [5, §5],
107 citations
Journal Article•
TL;DR: In this paper, several combinatorial sums and some inflnite series which involve thereciprocalsofbinomialcoe-cients are dealt with and many binomialidentities as well as some polynomial identities are proved.
Abstract: In this paper, we deal with several combinatorial sums and some inflnite series whichinvolvethereciprocalsofbinomialcoe‐cients. Manybinomialidentitiesaswell as some polynomial identities are proved.
80 citations
Book•
1 Jan 2002
TL;DR: The binominal and multinomial distributions Bernoulli's arithmetical triangle in analysis were studied in this article, where the binomial distribution of the arithmical triangle was analyzed.
Abstract: Contents: The Figurate Numbers Three Combinatorial Rules The Combinatorial Numbers in India The Combinatorial Numbers in the West The Binomial Numbers Pascal's Treatise on the Arithmetical Triangle Pascal's Treatise, Part II, and assocaited tracts The Arithmetical Triangle in analysis The binominal and multinomial distributions Bernoulli's Ars conjectandi
56 citations
48 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 3 |
| 2020 | 1 |
| 2019 | 2 |
| 2018 | 6 |
| 2017 | 4 |
| 2016 | 5 |