نتایج جستجو برای: q binomial theorem

تعداد نتایج: 268774  

2008
ALAIN LASCOUX ERIC M. RAINS S. OLE WARNAAR

The Knop–Sahi interpolation Macdonald polynomials are inho-mogeneous and nonsymmetric generalisations of the well-known Macdonald polynomials. In this paper we apply the interpolation Macdonald polyno-mials to study a new type of basic hypergeometric series of type gl n. Our main results include a new q-binomial theorem, new q-Gauss sum, and several transformation formulae for gl n series.

2008
ALAIN LASCOUX

The Knop–Sahi interpolation Macdonald polynomials are inhomogeneous and nonsymmetric generalisations of the well-known Macdonald polynomials. In this paper we apply the interpolation Macdonald polynomials to study a new type of basic hypergeometric series of type gln. Our main results include a new q-binomial theorem, new q-Gauss sum, and several transformation formulae for gln series.

2006
Yongsheng Ding Yang Xu Da Ruan Yingjun Cao Paul P. Wang Howard G. Clark Alade Tokuta Hongbin Sun Kuangrong Hao Shihuang Shao Ying Zhu Hongfeng Wang Dingwei Wang Xiangfeng Zhang Lihong Ren Lingjuan Wang Chengjian Wei Shuai Huang Bao Liu Junhong Wang Jiajun Lai Yuhong Li Jie Lu Xiaowei Yang Guangquan Zhang Zui Zhang Chenggang Bai Chunmei Lin Yue He Hongchun Yuan Ying Chen Qinghai Chen Xiaohua Liu Chunyan Han Kaiqi Zou Xiaobei Liang Xinghua Liu Daoli Zhu Bingyong Tang Junxi Bi Tao Yu Qiang Li Xiaohong Liu Xianyi Zeng Ludovic Koehl

The Hankel transform of an integer sequence (an) is defined as a sequence formed by the determinants of the matrices An, where An is the upper-left submatrix of size n× n of the Hankel matrix A =  a0 a1 a2 a3 · · · a1 a2 a3 a4 · · · a2 a3 a4 a5 · · · .. .. .. .. . . .  . In this talk, methods in deriving the Hankel transform of Bell and other Bell-type numbers will be discussed, particu...

Journal: :Electr. J. Comb. 2011
Dennis Eichhorn James McLaughlin Andrew V. Sills

We give “hybrid” proofs of the q-binomial theorem and other identities. The proofs are “hybrid” in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the Identity Theorem) to prove the full version. We prove three somewhat unusual summation formulae, and use these to give hybrid proofs of a number of identities d...

Journal: :Int. J. Math. Mathematical Sciences 2005
Amir Akbary Qiang Wang

Let Fq be a finite field of q = pm elements with characteristic p. A polynomial P(x) ∈ Fq[x] is called a permutation polynomial of Fq if P(x) induces a bijective map from Fq to itself. In general, finding classes of permutation polynomials of Fq is a difficult problem (see [3, Chapter 7] for a survey of some known classes). An important class of permutation polynomials consists of permutation p...

Journal: :Symmetry 2022

We introduce two new subclasses of analytic functions in the open symmetric unit disc using a linear operator associated with q-binomial theorem. In addition, we discuss inclusion relations and properties preserving integral operators for these classes. This paper generalizes some known results, as well provides ones.

Journal: :Mathematics 2023

In this article, we make use of the q-binomial theorem to introduce and study two new subclasses ℵ(αq,q) ℵ(α,q) meromorphic functions in open unit disk U, that is, analytic punctured U∗=U\{0}={z:z∈Cand0<z<1}. We derive inclusion relations investigate an integral operator preserves which belong these function classes. addition, establish a strict inequality involving certain linear convolu...

2005
Olga Holtz Volker Mehrmann Hans Schneider

In this partly historical and partly research oriented note, we display a page of an unpublished mathematical diary of Helmut Wielandt’s for 1951. There he gives a new proof of a theorem due to H. S. A. Potter on the matrix equation AB = ωBA, which is related to the q-binomial theorem, and asks some further questions, which we answer. We also describe results by M. P. Drazin and others on this ...

1994
Alexander Berkovich Mikhail Nirenberg

The Hilbert space of an RSOS-model, introduced by Andrews, Baxter, and Forrester, can be viewed as a space of sequences (paths) {a0, a1, . . . , aL}, with aj-integers restricted by 1 ≤ aj ≤ ν, | aj − aj+1 |= 1, a0 ≡ s, aL ≡ r. In this paper we introduce different basis which, as shown here, has the same dimension as that of an RSOS-model. This basis appears naturally in the Bethe ansatz calcula...

Journal: :The Electronic Journal of Combinatorics 2012

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