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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)
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 6 ψ 6 bilateral summation formula. In other words, the Abel lemma spells out the telescoping nature of the 6 ψ 6 sum. We present a systematic approach to compute Abel pairs for bilateral and unilateral basic hypergeometric summation formulas(More)
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