Nancy S. S. Gu

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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)
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)
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)
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)
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