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- 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 one-to-one correspondence between doubly rooted plane trees and free Dyck paths, which implies a simple derivation of a relation between the… (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 2 , 4 3 ,. . .) 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… (More)

- 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)

- 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)

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 folklore , 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

- 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)

- Hilmi Volkan Demir, Vijit A. Sabnis, +7 authors Yu-Min Houng
- 2003

Current optical-electronic-optical conversion (o-e-o) technology [1] requires propagating high-speed signals in the electronic domain and cascading separately packaged electronic and optoelectronic devices, resulting in increased cost, size, weight, power consumption, and heat radiation. For o-e-o conversion without the use of conventional electronics, we… (More)

- N. Li, X. Lin-Shi, P. Lefranc, E. Godoy, A. Jaafar, B. Allard
- Proceedings of the 2011 14th European Conference…
- 2011

This paper presents the application of fixed frequency (or indirect) Sliding Mode Control (SMC) to the DC-DC Single-Ended Primary Inductor Converter (SEPIC) which can operate in both step-up and step-down modes. Simulation and experimental studies are conducted. Two laboratory prototypes have been made: one with a switching frequency of 20kHz uses a DSP… (More)

This list is a compilation of combinatorial structures enumerated by the k-Catalan numbers C k n = 1 kn + 1 kn + 1 n = 1 (k − 1)n + 1 kn n for any positive integers k and n. We start by giving known combinatorial structures, together with references to where a proof can be found. The remainder of the list consists of new structures that are generalizations… (More)

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