Results 11 to 20 of about 90,542 (255)
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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Two permutation classes enumerated by the central binomial coefficients [PDF]
, 2013 We define a map between the set of permutations that avoid either the four patterns $3214,3241,4213,4231$ or $3124,3142,4123,4132$, and the set of Dyck prefixes. This map, when restricted to either of the two classes, turns out to be a bijection that allows us to determine some notable features of these permutations, such as the distribution of the ...
BARNABEI, MARILENA +2 more
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Factors of certain sums involving central q-binomial coefficients [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021 Recently, Ni and Pan proved a $q$-congruence on certain sums involving central $q$-binomial coefficients, which was conjectured by Guo. In this paper, we give a generalization of this $q$-congruence and confirm another $q$-congruence, also conjectured by Guo.
Guo, Victor J. W., Wang, Su-Dan
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Results in Nonlinear Analysis, 2021 In the paper, with the aid of the series expansions of the square or cubic of the arcsine function, the authors establish several possibly new combinatorial identities containing the ratio of two central binomial coefficients which are related to the ...
Feng Qi, Chao-Ping Chen , Dongkyu Lim
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Moments of the Negative Multinomial Distribution
Mathematical and Computational Applications, 2023 The negative multinomial distribution appears in many areas of applications such as polarimetric image processing and the analysis of longitudinal count data.
Frédéric Ouimet
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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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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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On a divisor of the central binomial coefficient [PDF]
The Ramanujan Journal, 2021 It is well known that for all $n\geq1$ the number $n+ 1$ is a divisor of the central binomial coefficient ${2n\choose n}$. Since the $n$th central binomial coefficient equals the number of lattice paths from $(0,0)$ to $(n,n)$ by unit steps north or east, a natural question is whether there is a way to partition these paths into sets of $n+ 1$ paths or
Matthew Just, Maxwell Schneider
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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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Some congruences involving central q-binomial coefficients
Advances in Applied Mathematics, 2010 16 pages, detailed proofs of Theorems 4.1 and 4.3 are added, to appear in Adv.
Guo, Victor J. W., Zeng, Jiang
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