Results 171 to 180 of about 42,989 (212)
Identities containing Gaussian binomial coefficients
Discrete Mathematics, 1989 Identities containing the Gaussian binomial \(\binom{n}{r}\) are obtained. From these results, we deduce some identities of the combinatorial analysis which contain the binomial coefficient \(\binom{n}{r}\).
Armel Mercier
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Gaussian Binomial Coefficients in Group Theory, Field Theory, and Topology
The American Mathematical Monthly, 2022 In this article, we offer group-theoretic, field-theoretic, and topological interpretations of the Gaussian binomial coefficients and their sum. For a finite $p$-group $G$ of rank $n$, we show that the Gaussian binomial coefficient $\binom{n}{k}_p$ is the number of subgroups of $G$ that are minimally expressible as an intersection of $n - k$ maximal ...
Sunil K. Chebolu, Keir Lockridge
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Gaussian Binomial Coefficients with Negative Arguments [PDF]
Annals of Combinatorics, 2019 Loeb showed that a natural extension of the usual binomial coefficient to negative (integer) entries continues to satisfy many of the fundamental properties. In particular, he gave a uniform binomial theorem as well as a combinatorial interpretation in terms of choosing subsets of sets with a negative number of elements. We show that all of this can be
Sam Formichella, Armin Straub
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Gaussian binomial coefficients modulo cyclotomic polynomials
Journal of Number Theory, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yan Li, Daeyeoul Kim, Lianrong Ma
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A probabilistic interpretation of the Gaussian binomial coefficients [PDF]
Journal of Applied Probability, 2017 Abstract We present a stand-alone simple proof of a probabilistic interpretation of the Gaussian binomial coefficients by conditioning a random walk to hit a given lattice point at a given time.
Takis Konstantopoulos, Linglong Yuan
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A Fibonacci Analogue of Gaussian Binomial Coefficients
The Fibonacci Quarterly, 1974 Gerald L. Alexanderson +1 more
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Evaluation of sums involving Gaussian q-binomial coefficients with rational weight functions
International Journal of Number Theory, 2015 We consider sums of the Gaussian [Formula: see text]-binomial coefficients with a parametric rational weight function. We use the partial fraction decomposition technique to prove the claimed results. We also give some interesting applications of our results to certain generalized Fibonomial sums weighted with finite products of reciprocal Fibonacci or
Emrah Kılıç, Helmut Prodinger
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