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Journal articles on the topic 'Q-binomial'

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Published: 24 April 2022

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1

Si-cong, Jing, and Fan Hong-yi. "q-deformed binomial state." Physical Review A 49, no. 4 (April 1, 1994): 2277–79. http://dx.doi.org/10.1103/physreva.49.2277.

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2

Chou, Wun-Seng. "Binomial permutations of finite fields." Bulletin of the Australian Mathematical Society 38, no. 3 (December 1988): 325–27. http://dx.doi.org/10.1017/s0004972700027659.

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3

Guo, Victor J. W., and C. Krattenthaler. "Some divisibility properties of binomial and q -binomial coefficients." Journal of Number Theory 135 (February 2014): 167–84. http://dx.doi.org/10.1016/j.jnt.2013.08.012.

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4

Pan, Hao. "Factors of some lacunary $$q$$ q -binomial sums." Monatshefte für Mathematik 172, no. 3-4 (October 20, 2013): 387–98. http://dx.doi.org/10.1007/s00605-013-0515-0.

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5

Butler, Lynne M. "The q-log-concavity of q-binomial coefficients." Journal of Combinatorial Theory, Series A 54, no. 1 (May 1990): 54–63. http://dx.doi.org/10.1016/0097-3165(90)90005-h.

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6

Obad, Alaa Mohammed, Asif Khan, Kottakkaran Sooppy Nisar, and Ahmed Morsy. "q-Binomial Convolution and Transformations of q-Appell Polynomials." Axioms 10, no. 2 (April 19, 2021): 70. http://dx.doi.org/10.3390/axioms10020070.

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In this paper, binomial convolution in the frame of quantum calculus is studied for the set Aq of q-Appell sequences. It has been shown that the set Aq of q-Appell sequences forms an Abelian group under the operation of binomial convolution. Several properties for this Abelian group structure Aq have been studied. A new definition of the q-Appell polynomials associated with a random variable is proposed. Scale transformation as well as transformation based on expectation with respect to a random variable is used to present the determinantal form of q-Appell sequences.
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7

Charalambides, Charalambos A. "The q-Bernstein basis as a q-binomial distribution." Journal of Statistical Planning and Inference 140, no. 8 (August 2010): 2184–90. http://dx.doi.org/10.1016/j.jspi.2010.01.014.

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8

Yalcin, Femin, and Serkan Eryilmaz. "q-geometric and q-binomial distributions of order k." Journal of Computational and Applied Mathematics 271 (December 2014): 31–38. http://dx.doi.org/10.1016/j.cam.2014.03.025.

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9

JING, SI-CONG, and HONG-YI FAN. "ON THE STATISTICS OF SU(1, 1)q and SU(2)q COHERENT STATES." Modern Physics Letters A 10, no. 08 (March 14, 1995): 687–94. http://dx.doi.org/10.1142/s0217732395000739.

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We find that the SU (2)q coherent state and SU (1, 1)q coherent state in the sense of statistics can be classified as q-binomial state and q-negative binomial state, respectively. Their relations with the q-Euler distribution and q-Heine distribution are discussed.
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10

Luca, Florian. "Perfect powers in q-binomial coefficients." Acta Arithmetica 151, no. 3 (2012): 279–92. http://dx.doi.org/10.4064/aa151-3-4.

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11

Pak, Igor, and Greta Panova. "Strict unimodality of q-binomial coefficients." Comptes Rendus Mathematique 351, no. 11-12 (June 2013): 415–18. http://dx.doi.org/10.1016/j.crma.2013.06.008.

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12

Zudilin, Wadim. "Congruences for $${\varvec{q}}$$-Binomial Coefficients." Annals of Combinatorics 23, no. 3-4 (November 2019): 1123–35. http://dx.doi.org/10.1007/s00026-019-00461-8.

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Abstract We discuss q-analogues of the classical congruence $$\left( {\begin{array}{c}ap\\ bp\end{array}}\right) \equiv \left( {\begin{array}{c}a\\ b\end{array}}\right) \pmod {p^3}$$apbp≡ab(modp3), for primes $$p>3$$p>3, as well as its generalisations. In particular, we prove related congruences for (q-analogues of) integral factorial ratios.
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13

Chung, Won-Sang, Ki-Soo Chung, Hye-Jung Kang, and Nan-Young Choi. "q-deformed probability and binomial distribution." International Journal of Theoretical Physics 34, no. 11 (November 1995): 2165–70. http://dx.doi.org/10.1007/bf00673832.

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14

Zeiner, Martin. "Convergence properties of the q-deformed binomial distribution." Applicable Analysis and Discrete Mathematics 4, no. 1 (2010): 66–80. http://dx.doi.org/10.2298/aadm100217016z.

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We consider the q-deformed binomial distribution introduced by S.C. Jing 1994: The q-deformed binomial distribution and its asymptotic behaviour, J. Phys. A 27 (2) (1994), 493{499 and W.S. Chung et al.: q-deformed probability and binomial distribution, Internat. J. Theoret. Phys. 34 (11) (1995), 2165{2170 and establish several convergence results involving the Euler and the exponential distribution; some of them are q-analogues of classical results.
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15

Cao, Jian, Hari M. Srivastava, Hong-Li Zhou, and Sama Arjika. "Generalized q-Difference Equations for q-Hypergeometric Polynomials with Double q-Binomial Coefficients." Mathematics 10, no. 4 (February 11, 2022): 556. http://dx.doi.org/10.3390/math10040556.

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In this paper, we apply a general family of basic (or q-) polynomials with double q-binomial coefficients as well as some homogeneous q-operators in order to construct several q-difference equations involving seven variables. We derive the Rogers type and the extended Rogers type formulas as well as the Srivastava-Agarwal-type bilinear generating functions for the general q-polynomials, which generalize the generating functions for the Cigler polynomials. We also derive a class of mixed generating functions by means of the aforementioned q-difference equations. The various results, which we have derived in this paper, are new and sufficiently general in character. Moreover, the generating functions presented here are potentially applicable not only in the study of the general q-polynomials, which they have generated, but indeed also in finding solutions of the associated q-difference equations. Finally, we remark that it will be a rather trivial and inconsequential exercise to produce the so-called (p,q)-variations of the q-results, which we have investigated here, because the additional forced-in parameter p is obviously redundant.
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16

Kiliç, Emrah, and Ilker Akkus. "On Fibonomial sums identities with special sign functions: analytically q-calculus approach." Mathematica Slovaca 68, no. 3 (June 26, 2018): 501–12. http://dx.doi.org/10.1515/ms-2017-0120.

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Abstract Recently Marques and Trojovsky [On some new identities for the Fibonomial coefficients, Math. Slovaca 64 (2014), 809–818] presented interesting two sum identities including the Fibonomial coefficients and Fibonacci numbers. These sums are unusual as they include a rare sign function and their upper bounds are odd. In this paper, we give generalizations of these sums including the Gaussian q-binomial coefficients. We also derive analogue q-binomial sums whose upper bounds are even. Finally we give q-binomial sums formulæ whose weighted functions are different from the earlier ones. To prove the claimed results, we analytically use q-calculus.
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17

Guo, Victor J. W., Frédéric Jouhet, and Jiang Zeng. "Factors of alternating sums of products of binomial and q-binomial coefficients." Acta Arithmetica 127, no. 1 (2007): 17–31. http://dx.doi.org/10.4064/aa127-1-2.

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18

Wang, Xiaoyuan, and Wenchang Chu. "Polynomial argument for $q$-binomial cubic sums*." Hiroshima Mathematical Journal 48, no. 2 (July 2018): 189–202. http://dx.doi.org/10.32917/hmj/1533088834.

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19

Chu, Wenchang, Chenying Wang, and Wenlong Zhang. "Partial Fractions and q-Binomial Determinant Identities." Cubo (Temuco) 12, no. 3 (2010): 1–12. http://dx.doi.org/10.4067/s0719-06462010000300001.

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20

Yun, Ma, and Zhang Youlin. "Q control charts for negative binomial distribution." Computers & Industrial Engineering 31, no. 3-4 (December 1996): 813–16. http://dx.doi.org/10.1016/s0360-8352(96)00260-4.

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21

Berkovich, Alexander, and S. Ole Warnaar. "Positivity preserving transformations for $q$-binomial coefficients." Transactions of the American Mathematical Society 357, no. 6 (December 10, 2004): 2291–351. http://dx.doi.org/10.1090/s0002-9947-04-03680-3.

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22

Garvan, Frank, and Dennis Stanton. "Sieved partition functions and $q$-binomial coefficients." Mathematics of Computation 55, no. 191 (September 1, 1990): 299. http://dx.doi.org/10.1090/s0025-5718-1990-1023761-1.

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23

Garvan, Frank, and Dennis Stanton. "Sieved Partition Functions and q-Binomial Coefficients." Mathematics of Computation 55, no. 191 (July 1990): 299. http://dx.doi.org/10.2307/2008807.

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24

Kupershmidt, Boris A. "q-Newton Binomial: From Euler To Gauss." Journal of Nonlinear Mathematical Physics 7, no. 2 (January 2000): 244–62. http://dx.doi.org/10.2991/jnmp.2000.7.2.8.

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25

Kato, Akishi, Yuma Mizuno, and Yuji Terashima. "Quiver Mutation Sequences and $q$-Binomial Identities." International Mathematics Research Notices 2018, no. 23 (May 29, 2017): 7335–58. http://dx.doi.org/10.1093/imrn/rnx108.

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26

Clark, W. Edwin. "q-Analogue of a binomial coefficient congruence." International Journal of Mathematics and Mathematical Sciences 18, no. 1 (1995): 197–200. http://dx.doi.org/10.1155/s016117129500024x.

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27

Gerhold, Stefan, and Martin Zeiner. "Convergence properties of Kemp’s q-binomial distribution." Sankhya A 72, no. 2 (August 2010): 331–43. http://dx.doi.org/10.1007/s13171-010-0019-0.

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28

Fishel, Susanna. "Nonnegativity results for generalized q-binomial coefficients." Discrete Mathematics 147, no. 1-3 (December 1995): 121–37. http://dx.doi.org/10.1016/0012-365x(94)00231-7.

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29

Davis, Reid, and Carl Wagner. "Covering algebras and q-binomial generating functions." Discrete Mathematics 128, no. 1-3 (April 1994): 95–111. http://dx.doi.org/10.1016/0012-365x(94)90106-6.

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30

Stanley, Richard P., and Fabrizio Zanello. "Some Asymptotic Results on q-Binomial Coefficients." Annals of Combinatorics 20, no. 3 (May 23, 2016): 623–34. http://dx.doi.org/10.1007/s00026-016-0319-8.

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31

Bhatia, Rejendra, and Ludwig Elsner. "The q-binomial theorem and spectral symmetry." Indagationes Mathematicae 4, no. 1 (March 1993): 11–16. http://dx.doi.org/10.1016/0019-3577(93)90047-3.

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32

Guo, Victor J. W., and Jiang Zeng. "Some congruences involving central q-binomial coefficients." Advances in Applied Mathematics 45, no. 3 (September 2010): 303–16. http://dx.doi.org/10.1016/j.aam.2009.12.002.

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33

Liu, Ji-Cai, and Fedor Petrov. "Congruences on sums of q-binomial coefficients." Advances in Applied Mathematics 116 (May 2020): 102003. http://dx.doi.org/10.1016/j.aam.2020.102003.

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34

Klenke, Achim, and Lutz Mattner. "Stochastic ordering of classical discrete distributions." Advances in Applied Probability 42, no. 2 (June 2010): 392–410. http://dx.doi.org/10.1239/aap/1275055235.

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For several pairs (P, Q) of classical distributions on ℕ0, we show that their stochastic ordering P ≤stQ can be characterized by their extreme tail ordering equivalent to P({k*})/Q({k*}) ≥ 1 ≥ limk→k*P({k})/Q({k}), with k* and k* denoting the minimum and the supremum of the support of P + Q, and with the limit to be read as P({k*})/Q({k*}) for finite k*. This includes in particular all pairs where P and Q are both binomial (bn1,p1 ≤stbn2,p2 if and only if n1 ≤ n2 and (1 - p1)n1 ≥ (1 - p2)n2, or p1 = 0), both negative binomial (b−r1,p1 ≤stb−r2,p2 if and only if p1 ≥ p2 and p1r1 ≥ p2r2), or both hypergeometric with the same sample size parameter. The binomial case is contained in a known result about Bernoulli convolutions, the other two cases appear to be new. The emphasis of this paper is on providing a variety of different methods of proofs: (i) half monotone likelihood ratios, (ii) explicit coupling, (iii) Markov chain comparison, (iv) analytic calculation, and (v) comparison of Lévy measures. We give four proofs in the binomial case (methods (i)-(iv)) and three in the negative binomial case (methods (i), (iv), and (v)). The statement for hypergeometric distributions is proved via method (i).
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35

Ernst, Thomas. "Further results on multiple q-Eulerian integrals for various q-hypergeometric functions." Publications de l'Institut Math?matique (Belgrade) 108, no. 122 (2020): 63–77. http://dx.doi.org/10.2298/pim2022063e.

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We continue the study of single and multiple q-Eulerian integrals in the spirit of Exton, Driver, Johnston, Pandey, Saran and Erd?lyi. The method of proof is often the q-beta integral method with the correct q-power together with the q-binomial theorem. By the Totov method we can prove summation theorems as special cases of multiple q-Eulerian integrals. The Srivastava ? notation for q-hypergeometric functions is used to enable the shortest possible form of the long formulas. The various q-Eulerian integrals are in fact meromorphic continuations of the various multiple q-functions, suitable for numerical computations. In the end of the paper a generalization of the q-binomial theorem is used to find q-analogues of a multiple integral formulas for q-Kamp? de F?riet functions.
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36

AYAD, MOHAMED, KACEM BELGHABA, and OMAR KIHEL. "ON PERMUTATION BINOMIALS OVER FINITE FIELDS." Bulletin of the Australian Mathematical Society 89, no. 1 (March 28, 2013): 112–24. http://dx.doi.org/10.1017/s0004972713000208.

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AbstractLet ${ \mathbb{F} }_{q} $ be the finite field of characteristic $p$ containing $q= {p}^{r} $ elements and $f(x)= a{x}^{n} + {x}^{m} $, a binomial with coefficients in this field. If some conditions on the greatest common divisor of $n- m$ and $q- 1$ are satisfied then this polynomial does not permute the elements of the field. We prove in particular that if $f(x)= a{x}^{n} + {x}^{m} $ permutes ${ \mathbb{F} }_{p} $, where $n\gt m\gt 0$ and $a\in { \mathbb{F} }_{p}^{\ast } $, then $p- 1\leq (d- 1)d$, where $d= \gcd (n- m, p- 1)$, and that this bound of $p$, in terms of $d$ only, is sharp. We show as well how to obtain in certain cases a permutation binomial over a subfield of ${ \mathbb{F} }_{q} $ from a permutation binomial over ${ \mathbb{F} }_{q} $.
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37

Klenke, Achim, and Lutz Mattner. "Stochastic ordering of classical discrete distributions." Advances in Applied Probability 42, no. 02 (June 2010): 392–410. http://dx.doi.org/10.1017/s0001867800004122.

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For several pairs (P, Q) of classical distributions on ℕ0, we show that their stochastic ordering P ≤st Q can be characterized by their extreme tail ordering equivalent to P({k *})/Q({k *}) ≥ 1 ≥ lim k→k * P({k})/Q({k}), with k * and k * denoting the minimum and the supremum of the support of P + Q, and with the limit to be read as P({k *})/Q({k *}) for finite k *. This includes in particular all pairs where P and Q are both binomial (b n 1,p 1 ≤st b n 2,p 2 if and only if n 1 ≤ n 2 and (1 - p 1) n 1 ≥ (1 - p 2) n 2 , or p 1 = 0), both negative binomial (b − r 1,p 1 ≤st b − r 2,p 2 if and only if p 1 ≥ p 2 and p 1 r 1 ≥ p 2 r 2 ), or both hypergeometric with the same sample size parameter. The binomial case is contained in a known result about Bernoulli convolutions, the other two cases appear to be new. The emphasis of this paper is on providing a variety of different methods of proofs: (i) half monotone likelihood ratios, (ii) explicit coupling, (iii) Markov chain comparison, (iv) analytic calculation, and (v) comparison of Lévy measures. We give four proofs in the binomial case (methods (i)-(iv)) and three in the negative binomial case (methods (i), (iv), and (v)). The statement for hypergeometric distributions is proved via method (i).
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38

Silindir, Burcu, and Ahmet Yantir. "Gauss’s binomial formula and additive property of exponential functions on T(q,h)." Filomat 35, no. 11 (2021): 3855–77. http://dx.doi.org/10.2298/fil2111855s.

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In this article, we focus our attention on (q,h)-Gauss?s binomial formula from which we discover the additive property of (q; h)-exponential functions. We state the (q,h)-analogue of Gauss?s binomial formula in terms of proper polynomials on T(q,h) which own essential properties similar to ordinary polynomials. We present (q,h)-Taylor series and analyze the conditions for its convergence. We introduce a new (q,h)-analytic exponential function which admits the additive property. As consequences, we study (q,h)-hyperbolic functions, (q,h)-trigonometric functions and their significant properties such as (q,h)-Pythagorean Theorem and double-angle formulas. Finally, we illustrate our results by a first order (q,h)-difference equation, (q,h)-analogues of dynamic diffusion equation and Burger?s equation. Introducing (q,h)-Hopf-Cole transformation, we obtain (q,h)-shock soliton solutions of Burger?s equation.
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39

Kiliç, Emrah, and Helmut Prodinger. "Evaluation of sums involving products of Gaussian q-binomial coefficients with applications." Mathematica Slovaca 69, no. 2 (April 24, 2019): 327–38. http://dx.doi.org/10.1515/ms-2017-0226.

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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. Then these q-binomial identities will be transformed into Fibonomial sums as consequences.
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40

Pan, Hao, and Hui-Qin Cao. "A congruence involving products of q-binomial coefficients." Journal of Number Theory 121, no. 2 (December 2006): 224–33. http://dx.doi.org/10.1016/j.jnt.2006.02.004.

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41

Economou, Antonis, and Stella Kapodistria. "q-SERIES IN MARKOV CHAINS WITH BINOMIAL TRANSITIONS." Probability in the Engineering and Informational Sciences 23, no. 1 (November 13, 2008): 75–99. http://dx.doi.org/10.1017/s0269964809000084.

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We consider a single-server Markovian queue with synchronized services and setup times. The customers arrive according to a Poisson process and are served simultaneously. The service times are independent and exponentially distributed. At a service completion epoch, every customer remains satisfied with probability p (independently of the others) and departs from the system; otherwise, he stays for a new service. Moreover, the server takes multiple vacations whenever the system is empty.Some of the transition rates of the underlying two-dimensional Markov chain involve binomial coefficients dependent on the number of customers. Indeed, at each service completion epoch, the number of customers n is reduced according to a binomial (n, p) distribution. We show that the model can be efficiently studied using the framework of q-hypergeometric series and we carry out an extensive analysis including the stationary, the busy period, and the sojourn time distributions. Exact formulas and numerical results show the effect of the level of synchronization to the performance of such systems.
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42

Dousse, Jehanne, and Byungchan Kim. "An overpartition analogue of the q-binomial coefficients." Ramanujan Journal 42, no. 2 (September 10, 2015): 267–83. http://dx.doi.org/10.1007/s11139-015-9718-4.

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43

Ahmia, Moussa, and Hacène Belbachir. "Preserving log-concavity for p,q-binomial coefficient." Discrete Mathematics, Algorithms and Applications 11, no. 02 (April 2019): 1950017. http://dx.doi.org/10.1142/s1793830919500174.

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We study the log-concavity of a sequence of [Formula: see text]-binomial coefficients located on a ray of the [Formula: see text]-Pascal triangle for certain directions, and we establish the preserving log-concavity of linear transformations associated to [Formula: see text]-Pascal triangle.
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44

Zhang, Zhizheng, and Jun Wang. "Some properties of the (q,h)-binomial coefficients." Journal of Physics A: Mathematical and General 33, no. 42 (October 11, 2000): 7653–58. http://dx.doi.org/10.1088/0305-4470/33/42/312.

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45

Guo, Victor J. W., Ying-Jie Lin, Yan Liu, and Cai Zhang. "A q-analogue of Zhang’s binomial coefficient identities." Discrete Mathematics 309, no. 20 (October 2009): 5913–19. http://dx.doi.org/10.1016/j.disc.2009.04.008.

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46

Menon, K. V. "Note on some determinants of q-binomial numbers." Discrete Mathematics 61, no. 2-3 (September 1986): 337–41. http://dx.doi.org/10.1016/0012-365x(86)90108-1.

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47

Zhu, Bao-Xuan. "Positivity and continued fractions from the binomial transformation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, no. 03 (March 18, 2019): 831–47. http://dx.doi.org/10.1017/prm.2018.26.

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AbstractGiven a sequence of polynomials$\{x_k(q)\}_{k \ges 0}$, define the transformation$$y_n(q) = a^n\sum\limits_{i = 0}^n {\left( \matrix{n \cr i} \right)} b^{n-i}x_i(q)$$for$n\ges 0$. In this paper, we obtain the relation between the Jacobi continued fraction of the ordinary generating function ofyn(q) and that ofxn(q). We also prove that the transformation preservesq-TPr+1(q-TP) property of the Hankel matrix$[x_{i+j}(q)]_{i,j \ges 0}$, in particular forr= 2,3, implying ther-q-log-convexity of the sequence$\{y_n(q)\}_{n\ges 0}$. As applications, we can give the continued fraction expressions of Eulerian polynomials of typesAandB, derangement polynomials typesAandB, general Eulerian polynomials, Dowling polynomials and Tanny-geometric polynomials. In addition, we also prove the strongq-log-convexity of derangement polynomials typeB, Dowling polynomials and Tanny-geometric polynomials and 3-q-log-convexity of general Eulerian polynomials, Dowling polynomials and Tanny-geometric polynomials. We also present a new proof of the result of Pólya and Szegö about the binomial convolution preserving the Stieltjes moment property and a new proof of the result of Zhu and Sun on the binomial transformation preserving strongq-log-convexity.
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48

Shattuck, Mark. "Generalizations of Bell number formulas of spivey and Mező." Filomat 30, no. 10 (2016): 2683–94. http://dx.doi.org/10.2298/fil1610683s.

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We provide q-generalizations of Spivey?s Bell number formula in various settings by considering statistics on different combinatorial structures. This leads to new identities involving q-Stirling numbers of both kinds and q-Lah numbers. As corollaries, we obtain identities for both binomial and q-binomial coefficients. Our results at the same time also generalize recent r-Stirling number formulas of Mez?. Finally, we provide a combinatorial proof and refinement of Xu?s extension of Spivey?s formula to the generalized Stirling numbers of Hsu and Shiue. To do so, we develop a combinatorial interpretation for these numbers in terms of extended Lah distributions.
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49

Vyas, Yashoverdhan, Hari M. Srivastava, Shivani Pathak, and Kalpana Fatawat. "General Summation Formulas Contiguous to the q-Kummer Summation Theorems and Their Applications." Symmetry 13, no. 6 (June 21, 2021): 1102. http://dx.doi.org/10.3390/sym13061102.

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This paper provides three classes of q-summation formulas in the form of general contiguous extensions of the first q-Kummer summation theorem. Their derivations are presented by using three methods, which are along the lines of the three types of well-known proofs of the q-Kummer summation theorem with a key role of the q-binomial theorem. In addition to the q-binomial theorem, the first proof makes use of Thomae’s q-integral representation and the second proof needs Heine’s transformation. Whereas the third proof utilizes only the q-binomial theorem. Subsequently, the applications of these summation formulas in obtaining the general contiguous extensions of the second and the third q-Kummer summation theorems are also presented. Furthermore, the investigated results are specialized to give many of the known as well as presumably new q-summation theorems, which are contiguous to the three q-Kummer summation theorems. This work is motivated by the observation that the basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) gamma and q-hypergeometric functions and basic (or q-) hypergeometric polynomials, are applicable particularly in several diverse areas including Number Theory, Theory of Partitions and Combinatorial Analysis as well as in the study of Combinatorial Generating Functions. Just as it is known in the theory of the Gauss, Kummer (or confluent), Clausen and the generalized hypergeometric functions, the parameters in the corresponding basic or quantum (or q-) hypergeometric functions are symmetric in the sense that they remain invariant when the order of the p numerator parameters or when the order of the q denominator parameters is arbitrarily changed. A case has therefore been made for the symmetry possessed not only by hypergeometric functions and basic or quantum (or q-) hypergeometric functions, which are studied in this paper, but also by the symmetric quantum calculus itself.
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Chu, Wenchang, and Emrah Kılıç. "Q-binomial formulae of Dixon's type and the Fibonomial sums." Applicable Analysis and Discrete Mathematics, no. 00 (2020): 16. http://dx.doi.org/10.2298/aadm190406016c.

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Abstract:
Cubic sums of the Gaussian q-binomial coefficients with certain weight functions will be evaluated in this paper. To realize this, we will derive two remarkable formulae by means of the Carlitz-Sears transformation on terminating well-poised q-series. As consequences, several summation formulae on Fibonomial coefficients are presented by specializing the value of base q in our q-series identities.
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