Results 41 to 50 of about 160,421 (323)
On the divisibility of binomial coefficients
Ars Mathematica Contemporanea, 2020 In Pacific J. Math. 292 (2018), 223-238, Shareshian and Woodroofe asked if for every positive integer $n$ there exist primes $p$ and $q$ such that, for all integers $k$ with $1 \leq k \leq n-1$, the binomial coefficient $\binom{n}{k}$ is divisible by at least one of $p$ or $q$. We give conditions under which a number $n$ has this property and discuss a
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Statistics on Lattice Walks and q-Lassalle Numbers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 This paper contains two results. First, I propose a $q$-generalization of a certain sequence of positive integers, related to Catalan numbers, introduced by Zeilberger, see Lassalle (2010).
Lenny Tevlin
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On divisibility of binomial coefficients
Discrete Mathematics, 1994 Let \(p\) be a prime and \(A(n,p)\) the \(p^ n\times p^ n\)-matrix with entries \(a_{ij}= \left(\begin{smallmatrix} i\\ j\end{smallmatrix}\right)\text{ mod }p\) for \(0\leq i,j< p^ n\). It is shown that \(A(n,p)\) is the \(n\)-fold tensor product of \(A(1,p)\) with itself. As an application a short proof is given that there are precisely \(\left(\begin{
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A new generalization of binomial coefficients
, 2013 Let $t$ be a fixed parameter and $x$ some indeterminate. We give some properties of the generalized binomial coefficients $\genfrac{}{0pt}{}{x}{k}$ inductively defined by $k/x \genfrac{}{0pt}{}{x}{k}= t\genfrac{}{0pt}{}{x-1}{k-1} +(1-t)\genfrac{}{0pt ...
Lassalle, Michel
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occumb: An R package for site occupancy modeling of eDNA metabarcoding data
Population Ecology, EarlyView.This study introduces a new R package, occumb, for the convenient application of site occupancy modeling using environmental DNA (eDNA) metabarcoding data. We outline a data analysis workflow, including data setup, model fitting, model assessment, and comparison of potential study settings based on model predictions, all of which can be performed using
Keiichi Fukaya, Yuta Hasebe
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An overpartition analogue of the $q$-binomial coefficients [PDF]
, 2014 We define an overpartition analogue of Gaussian polynomials (also known as $q$-binomial coefficients) as a generating function for the number of overpartitions fitting inside the $M \times N$ rectangle.
Dousse, Jehanne, Kim, Byungchan
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h analogue of Newton's binomial formula
, 1998 In this letter, the $h$--analogue of Newton's binomial formula is obtained in the $h$--deformed quantum plane which does not have any $q$--analogue. For $h=0$, this is just the usual one as it should be. Furthermore, the binomial coefficients reduce to $\
Benaoum H B +8 more
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Population Ecology, EarlyView.We investigate the seasonal dynamics of two freshwater snails, Biomphalaria straminea and Melanoides tuberculata, in artificial reservoirs of the Brazilian semiarid region. Despite regulated hydrology, B. straminea exhibited strong seasonal fluctuations associated with dry periods, while M. tuberculata maintained stable populations throughout the year,
Lucas Henrique Sousa da Silva +6 more
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Negation of binomial coefficients
Discrete Mathematics, 2008 We extend the concept of a binomial coefficient to all integer values of its parameters. Our approach is purely algebraic, but we show that it is equivalent to the evaluation of binomial coefficients by means of the @C-function. In particular, we prove that the traditional rule of ''negation'' is wrong and should be substituted by a slightly more ...
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A variation on bisecting the binomial coefficients
, 2018 In this paper, we present an algorithm which allows us to search for all the bisections for the binomial coefficients $\{\binom{n}{k} \}_{k=0,...,n}$ and include a table with the results for all $n\le 154$. Connections with previous work on this topic is
Ionascu, Eugen J.
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