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.

• Study combinatorial structures by using formal grammars.We provided new theories and methods for the study of permutation statistics.
• 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.

Research Fields: Combinatorics, Mathematical Chemistry