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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, Nelson Y. Li, Louis W. Shapiro, Sherry H. F. Yan
- Eur. J. Comb.
- 2007

We give a combinatorial interpretation of a matrix identity on Catalan numbers and the sequence (1, 4, 4, 4, . . .) which has been derived by Shapiro, Woan and Getu by using Riordan arrays. By giving a bijection between weighted partial Motzkin paths with an elevation line and weighted free Motzkin paths, we find a matrix identity on the number of weighted… (More)

The aim in this paper is to collect in one place a list of currently known and new structures enumerated by the k-ary numbers. Some of the structures listed already exist in the folk-lore, especially those that are easy generalizations of known combinatorial structures enumerated by the Catalan numbers. We will provide outlines on how the proofs for the… (More)

- Nelson Y. Li, Toufik Mansour
- Eur. J. Comb.
- 2008

- Silvia Heubach, Nelson Y. Li, Toufik Mansour
- Discrete Mathematics
- 2008

Many interesting combinatorial objects are enumerated by the k-Catalan numbers, one possible generalization of the Catalan numbers. We will present a new combinatorial object that is enumerated by the k-Catalan numbers, staircase tilings. We give a bijection between staircase tilings and k-good paths, and between k-good paths and k-ary trees. In addition,… (More)

- William Y. C. Chen, Nelson Y. Li, Louis W. Shapiro
- Discrete Applied Mathematics
- 2007

We introduce the notion of doubly rooted plane trees and give a decomposition of these trees, called the butterfly decomposition which turns out to have many applications. From the butterfly decomposition we obtain a oneto-one correspondence between doubly rooted plane trees and free Dyck paths, which implies a simple derivation of a relation between the… (More)

- Vít Jelínek, Nelson Y. Li, Toufik Mansour, Sherry H. F. Yan
- Electr. J. Comb.
- 2006

In this paper, we consider matchings avoiding partial patterns 1123 and 1132. We give a bijection between 1123-avoiding matchings with n edges and nonnegative lattice paths from (0, 2) to (2n, 0). As a consequence, the refined enumeration of 1123-avoiding matchings can be reduced to the enumeration of certain lattice paths. Another result of this paper is a… (More)

Dept. of Mathematics, California State University Los Angeles, Los Angeles, CA 90032, USA. Center for Combinatorics, LPMC, Nankai University, 300071 Tianjin, P.R. China. The High School Affiliated to Renmin University of China, Renmin University of China, 100080 Beijing, P.R. China. Department of Mathematics, Haifa University, 31905 Haifa, Israel.… (More)

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