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- Sen-Peng Eu, Shu-Chung Liu, Yeong-Nan Yeh
- Discrete Mathematics
- 2004

Over all plane trees with n edges, the total number of vertices with odd degree is twice the number of those with odd outdegree. Deutsch and Shapiro posed the problem of 3nding a direct two-to-one… (More)

- Sen-Peng Eu, Shu-Chung Liu, Yeong-Nan Yehc
- 2002

In this paper we introduce two new expansions for the generating functions of Catalan numbers and Motzkin numbers. The novelty of the expansions comes from writing the Taylor remainder as a… (More)

- Sen-Peng Eu, Tung-Shan Fu
- 2007

The notion of cyclic sieving phenomenon was introduced by Reiner, Stanton, and White as a generalization of Stembridge’s q = −1 phenomenon. The generalized cluster complexes associated to root… (More)

- Sen-Peng Eu, Tung-Shan Fu, Yeong-Nan Yeh
- J. Comb. Theory, Ser. A
- 2005

In this paper we prove a strengthening of the classical Chung-Feller theorem and a weighted version for Schröder paths. Both results are proved by refined bijections which are developed from the… (More)

- Sen-Peng Eu, Tung-Shan Fu
- Electr. J. Comb.
- 2005

Based on a bijection between domino tilings of an Aztec diamond and nonintersecting lattice paths, a simple proof of the Aztec diamond theorem is given in terms of Hankel determinants of the large… (More)

- Sen-Peng Eu, Shu-Chung Liu, Yeong-Nan Yeh
- Eur. J. Comb.
- 2008

In this paper, we compute the congruences of Catalan and Motzkin numbers modulo 4 and 8. In particular, we prove the conjecture proposed by Deutsch and Sagan that no Motzkin number is a multiple of… (More)

- Drew Armstrong, Sen-Peng Eu
- Electr. J. Comb.
- 2008

For each skew shape we define a nonhomogeneous symmetric function, generalizing a construction of Pak and Postnikov [9]. In two special cases, we show that the coefficients of this function when… (More)

- Sen-Peng Eu, Tung-Shan Fu, Yeh-Jong Pan
- Electr. J. Comb.
- 2010

A cyclic polytope of dimension d with n vertices is a convex polytope combinatorially equivalent to the convex hull of n distinct points on a moment curve in R. In this paper, we prove the cyclic… (More)

- Szu-En Cheng, Sen-Peng Eu, Tung-Shan Fu
- Eur. J. Comb.
- 2007

It is known that the area of all Catalan paths of length n is equal to 4− ` 2n+1

The Wiener Index, or the Wiener Number, also known as the “sum of distances” of a connected graph, is one of the quantities associated with a molecular graph that correlates nicely to physical and… (More)