Gould-Hsu反演的多重形式

应用组合计算技巧,本文建立了 Gould-Hsu(1973)反演的多重形式.并概述了其对于多重序列变换、多元有理插值及多重组合恒等式的应用.     

环型排列与连贯的计数

本文应用纯粹组合推理,研究了在广泛的贯长与贯数限制下多重集合排列的枚举问题。建立了在恒等群、循环群和二面体群作用下的环型连贯的计数公式。给出了无限制条件的平面及空间的环型交错排列与连贯的计数结果。     

DIRECT PROOF OF THE DETERMINANT EXPRESSION FOR FLAGGED SKEW TABLEAUX

Flagged skew tableaux are generalizationa of Young tableaux in which each row (column)has an upper and lower bound on the entries. It has been shown that they are enumerated byflagged skew Schur functions. By introducing the dominance technique, we preeent an alternateproof for this conclusion directly.     

Gould-Hsu-Carlitz反演与Rogers-Ramanujan恒等式(Ⅰ)

本文将论述通过q-级数互反关系证明经典分拆恒等式的一般方法。应用Carlitz给出的Gould-Hsu反演的q-模拟,作者将建立一个重要的和式变换定理。作为例证:结合Jacobi三重积恒等式及组合计算技巧,给出Rogers-Ra-manujan恒等式一个新的简单推证。     

关于组合和的超几何级数方法

本文旨在通过精选的例证,阐明关于组合和计算的一种极受重视的有效方法,即超几何级数的嵌入法。最后一节对三种典型方法作了简要的比较分析,述及作者自己的成果及见解。     

ON THE LATTICE PATH METHOD IN CONVOLUTION-TYPE COMBINATORIAL IDENTITIES (II)—THE WEIGHTED COUNTING FUNCTION METHOD ON LATTICE PATHS

An independent method for paper [10]is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolutions for path counts are investigated, which yields some Vandermunde-type identities for multinomial and q — multinomial coefficients.     

MULTIFOLD ANALOGUES OF GOULD-HSU INVERSIONS AND THEIR APPLICATIONS

By means of difference calculus, a multifold analog of Gould-Hsu inversion is established. Asconcrete examples, some multifold inverse relations are presented. By developing a standard prooftechnique for combinatorial identities, we demonstrate Mohanty-Hanna's convolution formulas almostmechanically. In addition, an application of reciprocal formulas to interpolation process is alsosketched.