Results 21 to 30 of about 19,998 (234)
Delannoy numbers and Legendre polytopes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We construct an $n$-dimensional polytope whose boundary complex is compressed and whose face numbers for any pulling triangulation are the coefficients of the powers of $(x-1)/2$ in the $n$-th Legendre polynomial.
Gábor Hetyei
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Human and constructive proof of combinatorial identities: an example from Romik [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 It has become customary to prove binomial identities by means of the method for automated proofs as developed by Petkovšek, Wilf and Zeilberger. In this paper, we wish to emphasize the role of "human'' and constructive proofs in contrast with the ...
D. Merlini, R. Sprugnoli, M. C. Verri
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Journal of Water and Health, 2023 This study evaluated the results recorded at the Central Public Health Laboratory of Santa Catarina state (Brazil) concerning the investigation of Rotavirus (RVA) and Norovirus (NoVs) – genogroups GI and GII. Samples were taken from seawater, river water,
Andreza Mortari +6 more
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New congruences for central binomial coefficients
Advances in Applied Mathematics, 2010 Let p be a prime and let a be a positive integer. In this paper we determine $\sum_{k=0}^{p^a-1}\binom{2k}{k+d}/m^k$ and $\sum_{k=1}^{p-1}\binom{2k}{k+d}/(km^{k-1})$ modulo $p$ for all d=0,...,p^a, where m is any integer not divisible by p. For example, we show that if $p\not=2,5$ then $$\sum_{k=1}^{p-1}(-1)^k\frac{\binom{2k}k}k=-5\frac{F_{p-(\frac p5)}
TAURASO, ROBERTO, Sun, ZW
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Stirling's Approximation for Central Extended Binomial Coefficients [PDF]
The American Mathematical Monthly, 2014 Slight modification of journal version; title ...
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Products and Sums Divisible by Central Binomial Coefficients [PDF]
The Electronic Journal of Combinatorics, 2013 In this paper we study products and sums divisible by central binomial coefficients. We show that $$2(2n+1)\binom{2n}n\ \bigg|\ \binom{6n}{3n}\binom{3n}n\ \ \mbox{for all}\ n=1,2,3,\ldots.$$ Also, for any nonnegative integers $k$ and $n$ we have $$\binom {2k}k\ \bigg|\ \binom{4n+2k+2}{2n+k+1}\binom{2n+k+1}{2k}\binom{2n-k+1}n$$ and $$\binom{2k}k\ \bigg|\
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Series associated with harmonic numbers, Fibonacci numbers and central binomial coefficients $binom{2n}{n}$ [PDF]
Notes on Number Theory and Discrete MathematicsWe find various series that involve the central binomial coefficients $binom{2n}{n}$, harmonic numbers and Fibonacci numbers. Contrary to the traditional hypergeometric function _pF_q approach, our method utilizes a straightforward transformation to ...
Segun Olofin Akerele +1 more
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On certain congruences involving central binomial coefficients
Mathematica Montisnigri, 2023 Let p be an odd prime. In this paper, using some properties of Fibonacci numbers, reciprocal polynomials for Fibonacci polynomials, and Legendre symbol, we establish some congruences involving central binomial coefficient modulo p and p^2. We also give some new identities for hyperbolic functions.
Rachid Boumahdi +2 more
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Powers in Prime Bases and a Problem on Central Binomial Coefficients
Integers, 2015 12 ...
Holdum, Sebastian Tim +2 more
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Harmonic Series of Convergence Ratio “1/4" with Cubic Central Binomial Coefficients
AxiomsWe examine a useful hypergeometric transformation formula by means of the coefficient extraction method. A large class of “binomial/harmonic series” (of convergence ratio “1/4”) containing the cubic central binomial coefficients and harmonic numbers is ...
Chunli Li, Wenchang Chu
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