Riordan群的反演链及在组合和中的应用

利用函数复合关系,本文在Ｒｉｏｒｄａｎ群中引入Ｒｉｏｒｄａｎ反演链的概念及其Ｒｉｏｒ－ｄａｎ反演链存在的充要条件,给出计算组合和式的递推方法．进一步讨论了二项式系数所对应的Ｒｉｏｒｄａｎ反演链问题,建立了一个Ｒｉｏｒｄａｎ求和公式,该式蕴含了某些与Ｆｉｂｏｎａｃｃｉ数相关的恒等式在内的一系列组合恒等式     

拉格朗日反演的q模拟与Bailey引理的注记

本文主要揭示了Gessel Ira.等给出的拉格朗日反演的q—模拟形式与An-drews G.E.的Bailey引理之间的相互转化的联系,做为例证,给出了利用这些关系得到的古典超几何级数(hypergeometric series)变换和求和公式的新证明,同时得到了模5、7、9、27四个新的Roger’s-Ramanujan类型的恒等式,其具有十分重要的组合意义。     

Riemann引理的若干证法和推广

本文首先给出了Ｒｉｅｍａｎｎ引理及其三种证法；然后通过直接方法、变量替换方法和多项式逼近的方法分别进行了证明．最后给出了Ｒｉｅｍａｎｎ引理的推广及其证明。     

Julia引理和Bloch常数

改进了经典的Julia引理, 研究了Bloch函数的枝点并得到涉及枝点的Bloch常数的新的下界.     

随机环境中马氏链的Chacon-Ornstein定理

利用随机环境中马氏链的Hofp极大遍历引理和Brunel极大遍历引理,给出了随机环境中马氏链的Chacon-Ornstein定理和Chacon认证定理.     

关于Arasu和Ma的一个引理的注记

通过改进Ａｒａｓｕ和Ｍａ的一个引理,在没有自共轭条件的情形下得到了一个关于西罗子群的指数界的差集存在的必要条件,作为它的一个应用,首次得到了不依赖于自共轭条件的指数界,从而对ＭｃＦａｒｌａｎｄ族与Ｓｐｅｎｃｅ族差集证明了Ｌａｎｄｅｒ猜想。     

Boccardo和Orsina引理的推广及应用

给出Boccardo和Orsina一个技术引理的推广,并给出其在能量空间中非强制积分泛函极小的正则性中的应用.     

Extensions of the well-poised and elliptic well-poised Bailey lemma

We establish a number of extensions of the well-poised Bailey lemma and elliptic well-poised Bailey lemma. As application we prove some new transformation formulae for basic and elliptic hyper-geometric series, and embed some recent identities of Andrews, Berkovich and Spiridonov in a well-poised Bailey tree.     

The Bailey Lemma and Kostka Polynomials

Using the theory of Kostka polynomials, we prove an A _n–1 version of Bailey's lemma at integral level. Exploiting a new, conjectural expansion for Kostka numbers, this is then generalized to fractional levels, leading to a new expression for admissible characters of A⁽¹⁾ _n–1 and to identities for A-type branching functions.     

The Bailey transform and false theta functions

An empirical exploration of five of Ramanujan's intriguing false theta function identities leads to unexpected instances of Bailey's transform which, in turn, lead to many new identities for both false and partial theta functions. 2000 Mathematics Subject Classification Primary—33D15, 11P83 Partially supported by National Science Foundation Grant DMS 0457003. Supported by the Australian Research Council.     

Self-inverse Sheffer sequences and Riordan involutions

In this short note, we focus on self-inverse Sheffer sequences and involutions in the Riordan group. We translate the results of Brown and Kuczma on self-inverse sequences of Sheffer polynomials to describe all involutions in the Riordan group.     

A Higher Level Bailey Lemma: Proof and Application

In a recent letter, new representations were proposed for the pair of sequences (,), as defined formally by Bailey in his famous lemma. Here we extend and prove this result, providing pairs (,) labelled by the Lie algebra AN – 1, two nonnegative integers and k and a partition , whose parts do not exceed N – 1. Our results give rise to what we call a higher level Bailey lemma. As an application it is shown how this lemma can be applied to yield general q-series identities, which generalize some well-known results of Andrews and Bressoud.     

Decomposition and Group Theoretic Characterization of Pairs of Inverse Relations of the Riordan Type

A new solution to Riordans problem of combinatorial identities classification is presented. An algebgraic characterization of pairs of inverse relations of the Riordan type is given. The use of the integral representation approach for generating new types of combinatorial identities is demonstrated. Supported in part by the National Sciences and Engineering Research Council of Canada on Grant NSERC-108343.Mathematics Subject Classifications (2000) combinatorics, algebra.     

An A Bailey lemma and Rogers-Ramanujan-type identities

Using new -functions recently introduced by Hatayama et al. and by (two of) the authors, we obtain an A version of the classical Bailey lemma. We apply our result, which is distinct from the A Bailey lemma of Milne and Lilly, to derive Rogers-Ramanujan-type identities for characters of the W algebra.