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About 1,764 papers for “Binomial coefficient”

Binomial Coefficient Model

<vcard>BEGIN:vCard\VERSION:3.0\FN:Wolfgang Christian\TITLE:\ORG:Davidson College\ADR;TYPE=WORK,POSTAL,PARCEL:;;Department of Physics;PO Box 7133;Davidson;NC;28035;US\TEL;TYPE=Business:+704-984-2322\TEL;TYPE=:+\TEL;TYPE=FAX:+\EMAIL;TYPE=INTERNET,Work:wochristian@davidson.edu\EMAIL;TYPE=INTERNET,:\END:vCard</vcard> · The Physics Video Demonstration Database (Cornell University)

Cited by 0

On Binomial Coefficient Residues

Joe Roberts · Canadian Journal of Mathematics · 1957

The number of binomial coefficients , which are congruent to j , 0 ≤ j ≤ p − 1, modulo the prime number p is denoted by θ j ( n ). In this paper we give systems of simultaneous linear difference equations with constant coefficients whose solutions would yield the quantities θ j ( n ) explicitly.

Cited by 19Open access

87.34 Some binomial coefficient identities

Michael D. Hirschhorn · The Mathematical Gazette · 2003

An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.

Cited by 2

Binomial-coefficient multiples of irrationals

Terrence Adams, Karl Petersen · ArXiv.org · 1998

Denote by $x$ a random infinite path in the graph of Pascal's triangle (left and right turns are selected independently with fixed probabilities) and by $d_n(x)$ the binomial coefficient at the $n$'th level along the path $x$. Then for a dense $G_δ$ set of $θ$ in the unit interval, $\{d_n(x)θ\}$ is almost surely dense but not uniformly distributed modulo 1.

Cited by 0Open access

Functions of the Binomial Coefficient

Sean Plott · Scholarship @ Claremont (The Claremont Colleges) · 2008

available for noncommercial, educational purposes, provided that this copyright statement appears on the reproduced materials and notice is given that the copy-ing is by permission of the author. To disseminate otherwise or to republish re-quires written permission from the author. The well-known binomial coefficient is the building block of Pascal’s trian-gle. We explore the relationship between functions of the binomial coeffi-cient and Pascal’s triangle, providing proofs of connections between Cata-lan numbers, determinants, non-intersecting paths, and Baxter permuta-tions. Contents Abstract iii

Cited by 0Open access

Binomial Coefficient Computation: Recursion or Iteration

Yannis Manolopoulos · 2007

Binomial 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 for this purpose.

Cited by 0

Binomial^3: coefficient, equivalence, and complexities

Stipulanti, Manon · Open Repository and Bibliography (University of Liège) · 2023

In combinatorics on words, for two words u and v, the binomial coefficient (u,v) of u and v is the number of times v appears as a (scattered) subword of u. For example, with u=ababba and v=aba, there are (6,3)=15 ways to select 3 letters among 6, but only (u,v)=6 of them give back v. Generalizing famous binomial coefficients of integers, the word version has received a lot of attention within the combinatorics-on-words community. A few years ago, M. Rigo and P. Salimov introduced the notion of k-binomial equivalence: two words u and v are k-binomially equivalent if the binomial coefficients (u,x) and (v,x) are equal for all words x of length up to k. This is a refinement of the usual abelian equivalence and Simon's congruence. Very naturally, one can then associate the corresponding k-binomial complexity function which, for a given infinite word x, maps n to the number of length-n factors of x up to the k-binomial equivalence relation. In this talk, I present a broad overview of the theory of binomial coefficients, equivalence, and complexities, focusing on some recent results obtained by M. Rigo, M. Whiteland, and myself.

Cited by 0Open access

Note on a Binomial Coefficient Divisor

Matthew Just · Mathematics Magazine · 2023

SummaryLet n be a positive integer, and k and integer with 0≤k≤n. Let g be the greatest common divisor of k and n. We use the cycle construction to give a combinatorial proof that the fraction n/g divides the binomial coefficient (nk).

Cited by 0

Properties of the Central Binomial Coefficient

Béla Bollobás · Cambridge University Press eBooks · 2022

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