Results 181 to 190 of about 42,989 (212)
Quadratic sums of Gaussian q-binomial coefficients and Fibonomial coefficients
The Ramanujan Journal, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wenchang Chu, Emrah Kılıç
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Evaluation of sums involving products of Gaussian q-binomial coefficients with applications
Mathematica Slovaca, 2019 Abstract Sums of products of two Gaussian q-binomial coefficients, are investigated, one of which includes two additional parameters, with a parametric rational weight function. By means of partial fraction decomposition, first the main theorems are proved and then some corollaries of them are derived.
Emrah Kılıç, Helmut Prodinger
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On algebra and arithmetic of binomial and Gaussian coefficients
Chebyshevskii sbornik, 2019 Summary: In this paper we consider questions relating to algebraic and arithmetic properties of such binomial, polynomial and Gaussian coefficients. For the central binomial coefficients \(\binom{2p}{p}\) and \(\binom{2p-1}{p-1} \), a new comparability property modulo \(p^3 \cdot \left( 2p-1 \right)\), which is not equal to the degree of a prime number,
У. М. Пачев
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Projective Geometry over 픽1 and the Gaussian Binomial Coefficients
The American Mathematical Monthly, 2004 There is no field with only one element, yet there is a well-defined notion of what projective geometry over such a field means. This notion is familiar to experts and plays an interesting role behind the scenes in combinatorics and algebra, but it is rarely discussed as such.
Henry Cohn
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On theq-log-concavity of Gaussian binomial coefficients
Monatshefte f�r Mathematik, 1989 We give a combinatorial proof that\(\left[ {\begin{array}{*{20}c} a \\ k \\ \end{array} } \right]_q \left[ {\begin{array}{*{20}c} b \\ l \\ \end{array} } \right]_q - \left[ {\begin{array}{*{20}c} a \\ {k - 1} \\ \end{array} } \right]_q \left[ {\begin{array}{*{20}c} b \\ {l + 1} \\ \end{array} } \right]_q \) is a polynomial inq with nonnegative ...
Christian Krattenthaler
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The American Mathematical Monthly, 2000 (2000). A Unified Interpretation of the Binomial Coefficients, the Stirling Numbers, and the Gaussian Coefficients. The American Mathematical Monthly: Vol. 107, No. 10, pp. 901-910.
John Konvalina
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q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients
Russian Journal of Mathematical Physics, 2008 A purpose of this paper is to present a systemic study of some families of multiple q-Bernoulli numbers and polynomials by using the multivariate q-Volkenborn integral (= p-adic q-integral) on ℤ p . Moreover, the study of these higher-order q-Bernoulli numbers and polynomials implies some interesting q-analogs of ...
T. Kim
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Gaussian Binomial Coefficients at Roots of 1
, 2010 34.1.1. Let l be an integer ≥ 1. In this chapter we assume that the A-algebra R, with \(\phi :A \to R\) and with \({\rm{v}} = \phi (\upsilon )\), is such that R is an integral domain and the following ...
G. Lusztig
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A class of non-symmetric band determinants with the Gaussian q -binomial coefficients
Quaestiones Mathematicae, 2017 A class of symmetric band matrices of bandwidth 2r+1 with the binomial coefficients entries was studied earlier. We consider a class of non-symmetric band matrices with the Gaussian q-binomial coefficients whose upper bandwith is s and lower bandwith is r. We give explicit formulæ for the determinant, the inverse (along with its infinity-norm when q →1)
Talha Arıkan, Emrah Kılıç
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TURKISH JOURNAL OF MATHEMATICS, 2017 Summary: Sums of products of two Gaussian \(q \)-binomial coefficients with a parametric rational weight function are considered. The partial fraction decomposition technique is used to evaluate the sums in closed form. Interesting applications of these results to certain generalized Fibonomial and Lucanomial sums are provided.
Emrah Kılıç, Helmut Prodinger
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