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- Nancy S. S. Gu, Nelson Y. Li, Toufik Mansour
- Discrete Mathematics
- 2008

A 2-binary tree is a binary rooted tree whose root is colored black and the other vertices are either black or white. We present several bijections concerning different types of 2-binary trees as well as other combinatorial structures such as ternary trees, non-crossing trees, Schröder paths, Motzkin paths and Dyck paths. We also obtain a number of… (More)

- William Y. C. Chen, Wenchang Chu, Nancy S. S. Gu
- J. Comb. Theory, Ser. A
- 2006

where the q-shifted factorial is defined by (x; q)0 = 1 and (x; q)n = (1− x)(1 − qx) · · · (1− q x) for n = 1, 2, · · · with the following abbreviated multiple parameter notation [α, β, · · · , γ; q]∞ = (α; q)∞(β; q)∞ · · · (γ; q)∞. This identity has several important applications in combinatorial analysis, number theory and special functions. For the… (More)

- Nancy S. S. Gu, Helmut Prodinger
- Eur. J. Comb.
- 2009

According to the Fibonacci number which is studied by Prodinger et al., we introduce the 2-plane tree which is a planted plane tree with each of its vertices colored with one of two colors and qqppppppppppppppppp -free. The similarity of the enumeration between 2-plane trees and ternary trees leads us to build several bijections. Especially, we found a… (More)

- Nancy S. S. Gu, Helmut Prodinger, Stephan G. Wagner
- Eur. J. Comb.
- 2010

We consider plane trees whose vertices are given labels from the set {1, 2, . . . , k} in such a way that the sum of the labels along any edge is at most k + 1; it turns out that the enumeration of these trees leads to a generalization of the Catalan numbers. We also provide bijections between this class of trees and (k + 1)-ary trees as well as generalized… (More)

- Vincent Y. B. Chen, William Y. C. Chen, Nancy S. S. Gu
- Math. Comput.
- 2008

Chu has recently shown that the Abel lemma on summations by parts can serve as the underlying relation for Bailey’s 6ψ6 bilateral summation formula. In other words, the Abel lemma spells out the telescoping nature of the 6ψ6 sum. We present a systematic approach to compute Abel pairs for bilateral and unilateral basic hypergeometric summation formulas by… (More)

Resorting to the recursions satisfied by the polynomials which converge to the right hand sides of the Rogers-Ramanujan type identities given by Sills [17] and determinant method presented in [9], we obtain many new one-parameter generalizations of the Rogers-Ramanujan type identities, such as a generalization of the analytic versions of the first and… (More)

We introduce the Cauchy augmentation operator for basic hypergeometric series. Heine’s 2φ1 transformation formula and Sears’ 3φ2 transformation formula can be easily obtained by the symmetric property of some parameters in operator identities. The Cauchy operator involves two parameters, and it can be considered as a generalization of the operator T (bDq).… (More)

It is well known that many bilateral basic hypergeometric identities can be derived from unilateral identities. Using Cauchy’s method [5, 15, 20, 21] one may obtain bilateral basic hypergeometric identities from terminating unilateral identities. Starting with nonterminating unilateral basic hypergeometric series, Chen and Fu [8] developed a method to… (More)

- Nancy S. S. Gu, Li Guo
- Discrete Mathematics
- 2015

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