## 研究員 |   葉永南

 聯絡資訊 Email : mayeh$\color{red}{@}$math.sinica.edu.tw Phone:+886 2 2368-5999 ext. 629 Fax:    +886 2 2368-9771 相關連結 學歷 Ph.D. in Mathematics 美國紐約州立大學水牛城分校 (1983-1985) M.S. in Mathematics 美國紐約州立大學水牛城分校 (1981-1983) B.S. in Mathematics 台灣大學 (1974-1978) 研究專長 組合數學 數學化學

• Chairman the mathematical center, National Science of Council, Taiwan, R.O.C. 1995 -1997
• Visiting Scholar Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. 1991 -1992
• Associate Research Fellow Institute of Mathematics, Academia Sinica, Nankang, Taipei, Taiwan, R.O.C. 1987 -1990
• Post-doctoral Fellow University of Quebec at Montreal, Montreal, Canada. 1985 - 1987
• Research Fellow Institute of Mathematics, Academia Sinica, Nankang, Taipei, Taiwan, R.O.C.

• Outstanding Research Award, Academia Sinica, R.O.C., 2011~2014
• Outstanding Research Project Award, National Science Council, R.O.C., 2009~2012
• Research Award, National Science Council, R.O.C., 2006~2008
• The first class Research Award, National Science Council, R.O.C., 2002~2005
• Research Award, National Science Council, R.O.C., 1998~2001
• Outstanding Research Award, National Science Council, R.O.C., 1994, 1995, 1996, 1997
• Excellent Paper Award, Association of Computer Science, R.O.C., 1990
• Excellent Research Award, National Science Council, R.O.C., 1989, 1991, 1993

Dr. Yeh's major research interest is on discrete mathematics, Mathematical Chemistry, Game Theory and Orthogonal Polynomials.

Combinatorics and its related fields With the rapid development of combinatorics, it takes great efforts of mathematicians to apply other mathematical areas on combinatorics systematically. Dr. Yeh's research concentrates on exploring the relations between combinatorics and other mathematical fields. Main aspects of his research are as follows.

•  Use generating functions to determine the property of congruence for combinatorial series.
• Study further properties on the Tutte polynomial and its application in terms of the critical bridge.
• Study the Whitney theorem on chromatic polynomial of signed graphs. By decomposition of incidence functions to interpret the convolution formulate of Tutte polynomial of matroids and characteristic polynomial of hyperplane arrangements.
• Apply the generalized cycle lemma to the fluctuation theory, as well to the structural parameters and Chung-Feller of combinatorial models.
• Find the hidden arithmetic properties of combinatorial series, such as unimodality, log-concativity, log-convexity, and Polya frequency.
• By analyzing the topological indices of molecular graphs, theoretically study the physical and chemical properties of molecules and predict the existence of certain molecules.

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