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Chemical Physics Letters, ISSN 0009-2614, 11/2019, Volume 735, p. 136769
•In the theoretical quantum mechanical studies, Gaunt coefficients are encountered.•Gaunt coefficients are associated with spherical harmonics.•Gaunt... 
Clebsch-Gordan coefficients | Gaunt coefficients | Binomial coefficients | Bessel functions | Molecular integrals | SLATER-TYPE ORBITALS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | OVERLAP | CHEMISTRY, PHYSICAL | COULOMB INTEGRALS
Journal Article
Magnetic Resonance in Chemistry, ISSN 0749-1581, 09/2018, Volume 56, Issue 9, pp. 799 - 802
The NMR intensity pattern of a nucleus split by N identical nuclei of spin 1/2 is given by the binomial coefficients. These are conveniently obtained from... 
11B | NMR | EPR | spin–spin splitting | 14N | 35Cl | multiplet pattern | spin-spin splitting | SPECTROSCOPY | B-11 | N-14 | Cl-35 | CHEMISTRY, PHYSICAL | H-2 | CHEMISTRY, MULTIDISCIPLINARY | Organic chemistry | Splitting | Nuclear magnetic resonance--NMR | Binomial coefficients | Equivalence | Polynomials | Nuclei
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 08/2017, Volume 227, pp. 70 - 83
In this paper, we deal with the problem of bisecting binomial coefficients. We find many (previously unknown) infinite classes of integers which admit... 
Binomial coefficients | Diophantine equations | Subset sum problem | MATHEMATICS, APPLIED | LINEAR BOOLEAN EQUATIONS | FORMULA
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 08/2017, Volume 227, p. 70
In this paper, we deal with the problem of bisecting binomial coefficients. We find many (previously unknown) infinite classes of integers which admit... 
Integers | Binomial coefficients | Binomial distribution | Cryptography | Combinatorics
Journal Article
Annals of Combinatorics, ISSN 0218-0006, 11/2019, Volume 23, Issue 3-4, pp. 1123 - 1135
Annals of Combinatorics 23 (2019), no. 3-4, 1123--1135 We discuss $q$-analogues of the classical congruence $\binom{ap}{bp}\equiv\binom{a}{b}\pmod{p^3}$, valid... 
Journal Article
The American Mathematical Monthly, ISSN 0002-9890, 03/2018, Volume 125, Issue 3, pp. 231 - 244
In this article, we use elementary methods to investigate continuous binomial coefficients: functions of the real variable x defined by way of the gamma... 
Primary 33B15 | Secondary 26E05 | MATHEMATICS | INTEGRAL ANALOG | SERIES
Journal Article
Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 06/2017, Volume 95, Issue 3, pp. 365 - 372
We investigate the monotonic characteristics of the generalised binomial coefficients (phinomials) based upon Euler's totient function. We show,... 
Euler function | monotony | generalised binomial coefficients | MATHEMATICS
Journal Article
Journal of the Korean Statistical Society, ISSN 1226-3192, 2018, Volume 48, Issue 2, pp. 248 - 264
Integer-valued time series models and their applications have attracted a lot of attention over the last years. In this paper, we introduce a class of... 
Empirical likelihood | Random coefficient INAR models | Negative binomial thinning | Conditional least squares | EMPIRICAL LIKELIHOOD INFERENCE | MODELS | TIME-SERIES | STATISTICS & PROBABILITY
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 12/2018, Volume 250, p. 276
In this paper, we present an algorithm which allows us to search for all the bisections for the binomial coefficients ... and include a table with the results... 
Binomial coefficients | Applied mathematics | Binomial distribution | Probability distribution | Coefficient of variation
Journal Article
Journal of Number Theory, ISSN 0022-314X, 02/2020, Volume 207, pp. 145 - 155
A practical number is a positive integer n such that every positive integer less than n can be written as a sum of distinct divisors of n. We prove that most... 
Binomial coefficient | Central binomial coefficient | Practical number | MATHEMATICS | DIVISORS
Journal Article
Analog Integrated Circuits and Signal Processing, ISSN 0925-1030, 6/2019, Volume 99, Issue 3, pp. 599 - 606
Journal Article
The American Mathematical Monthly, ISSN 0002-9890, 07/2015, Volume 122, Issue 7, pp. 636 - 644
We study some old and new problems involving divisors of the middle binomial coefficient . 
Binomial coefficients | ARTICLES | DIVISIBILITY | MATHEMATICS | Division | Tests, problems and exercises
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 12/2018, Volume 250, pp. 276 - 284
In this paper, we present an algorithm which allows us to search for all the bisections for the binomial coefficients {nk}k=0,…,n and include a table with the... 
Binomial coefficients | Algorithm | Congruence | POLYNOMIALS | MATHEMATICS, APPLIED | SYMMETRIC BOOLEAN FUNCTIONS | GREATEST COMMON DIVISOR | Algorithms
Journal Article
Sbornik Mathematics, ISSN 1064-5616, 2015, Volume 206, Issue 11, pp. 1524 - 1563
We describe the coefficient rings of universal formal group laws which arise in algebraic geometry, algebraic topology and their application to mathematical... 
Formal group law | Binomial coefficients | Hirzebruch genus | Addition law | MATHEMATICS | FUNCTIONAL-EQUATIONS | binomial coefficients | COMPLEX COBORDISM | addition law | formal group law | ELLIPTIC GENERA | Homomorphisms | Reduction | Algebra | Mathematical analysis | Topology | Coefficients | Rings (mathematics)
Journal Article
MAGNETIC RESONANCE IN CHEMISTRY, ISSN 0749-1581, 09/2018, Volume 56, Issue 9, pp. 798 - 798
The NMR intensity pattern of a nucleus split by N identical nuclei of spin 1/2 is given by the familiar binomial coefficients. These are conveniently obtained... 
SPECTROSCOPY | CHEMISTRY, PHYSICAL | CHEMISTRY, MULTIDISCIPLINARY | Organic chemistry | Splitting | Nuclear magnetic resonance--NMR | Binomial coefficients | Equivalence | Mathematical analysis | Chemists | Polynomials | Nuclei
Journal Article
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, ISSN 0308-2105, 2019, pp. 1 - 12
AbstractWe prove some congruences on sums involving fourth powers of centralq-binomial coefficients. As a conclusion, we confirm the following supercongruence... 
cyclotomic polynomials | q-analogue of Wolstenholme's binomial congruence | q-binomial coefficients | q-analogue of Morley's congruence | q-WZ method
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 11/2014, Volume 10, Issue 7, pp. 1729 - 1742
In this paper, we study a balancing problem of ordinary binomial coefficients. The diop-hantine equation $$ \left(\begin{array}{@{}c@{}} 0\\ k... 
Diophantine equations | binomial coefficients | balancing problems | MATHEMATICS | NUMBERS | EQUATION
Journal Article
Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 08/2018, Volume 158, pp. 228 - 253
In a previous paper, we studied an overpartition analogue of Gaussian polynomials as the generating function for overpartitions fitting inside an m×n... 
Overpartitions | Delannoy numbers | Gaussian polynomial | Over-[formula omitted]-binomial coefficient | q-Binomial coefficient | Combinatorial proofs | Finite versions of q-series identities | q-log concavity | Over-(q,t)-binomial coefficient | IDENTITY | MATHEMATICS | NUMBERS | Over-(q, t)-binomial coefficient
Journal Article
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