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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.

Email : mayeh AT
Phone:+886 2 2368-5999 ext. 629
Fax: +886 2 2368-9771

著作目錄 :

1.  The calculus of virtual species an K-species, Lecture Notes in Mathematics, Springer Verlag , 1234(1986), 351-369
2.  (with J. Labelle) Some combinatorics of the hypergeometric series, European Journal of Combinatorics , 6(1988-11), 593-605
3.  (with J. Labelle) The combinatorics of Laguerre, Charlier and Hermite polynomials revisited, Studies in Applied Mathematics , 80(1989-02), no. 1, 25-36
4.  (with J. Labelle) The relations between permutation groups and combinatorics species, Journal of Combinatorial Theory (series A) , 50(1989-03), 269-284
5.  (with J. Labelle) Dyck paths of knight moves, Discrete Applied Mathematics , 24(1989-08), 213-221
6.  (with J. Labelle) Combinatorial proof of some limit formulas involving orthogonal polynomials, Discrete Mathematics , 79(1990-01), 77-93
7.  (with J. Labelle) Generalized Dyck paths, Discrete Mathematics , 82(1990-05), 1-6
8.  (with F. Bergeron) The factoriality of the ring of S-species, Journal of combinatorial Theory (series A) , 55(1990-11), 194-203
9.  (with S. L. Lee ,Y. Luo and B. Sanan) Eigenvector and eigenvalues of some special graphs, IV. multilevel circulants, International Journal of Quantum Chemistry , 41(1992-01), 105-116
10.  (with I. Gutman and S. L. Lee and Y. L. Luo) Recent results in the theory of the Wiener number, Indian Journal of Chemistry , 32A(1993-08), 651-661
11.  (with B. Sagan and G. Ziegler) Maxmizing mobius functions on subsets of boolean algebras, Discrete Mathematics , 126(1994-03), 293-311
12.  (with A. Ivashchenko) Minimal graph of a torus, a projective plane and spheres. Some properties of minimal graphs of homotopy class, Discrete Mathematics , 126(1994-03), 171-178
13.  (with B. Chen) Some explanations of the Dobinski's formula, Studies in Applied Mathematics , 92(1994-07), 191-199
14.  (with W. Y. C. Chen and K. W. Lih) Cyclic tableaux and symmetric functions, Studies in Applied Mathematics , 94(1995-04), 327-339
15.  The generating polynomial and Euler characteristic of intersection graphs, Discrete Mathematics , 131(1994-08), 325-333
16.  (with I. Gutman) On the sum of all distances in composite graphs, Discrete Mathematics , 135(1994-12), 359-365
17.  (with I. Gessel and B. Sagan) Enumeration of trees by inversions, Journal of Graph Theory , 19(1995-07), 435-459
18.  (with B. Y. Yang) Zigging and zagging pentachains, Advances in Applied Mathematics , 16(1995-03), 72-94
19.  (with B. Gan) The Nim-like game and dynamic recurrence relations, Studies in Applied Mathematics , 95(1995-08), 213-228
20.  (with R. Servedio) A bijective proof on circular compositions, Bull. Inst. Math. , Academia Sinica , 23(1995), 283-293
21.  A remarkable endofunction involving compositions, Studies in Applied Mathematics , 95(1995-11), 419-432
22.  (with I. Gutman) On the sum of all distances in bipartite graphs, Mathematica Slovaca , 45(1995), 327-334
23.  (with B. Y. Yang) Chains of motley gems and their wiener indices, Proceedings of Tainan-Moscaw workshop,Tainan,Walter de Gruyter (1995), 0-0
24.  (with Y. W. Huang and B. Y. Yang) Wiener index of hexagonal carpets - From hexes to square grids, Southeast Asian Bulletin of Mathematics , 20(1996), 81-102
25.  (with I. Gutman and Chin-Mei Fu) Graph transformations which preserve the multiplicity of an eigenvalue, Discrete Applied Mathematics , 67(1996-05), 221-228
26.  (with B. Sagan and P. Zhang) The wiener polynomial of a graph, International Journal of Quantum Chemistry , 60(1996-12), 959-969
27.  (with W. Huang and B. Y. Yang) From ternary strings to wiener indices of benezoid chains, Discrete Applied Mathematics , 73(1997-03), 113-131
28.  (with S. C. Chang) The cardinality of the collection of maximum independent sets of a graph, Advances in Applied Mathematics , 18(1997-04), 286-299
29.  (with H. K. Hwang) Measures of distinctness for random partitions and compositions of an integer, Advances in Applied Mathematics , 19(1997-10), 378-414
30.  (with Li-Da Tong ! S.C. Liu) The tree with the minimum Wiener Number, International, Journal of Quantum Chemistry , 78(2000-06), 331-340
31.  (with H. K. Hwang ! B. Y. Yang) Presorting algorithms: an average-case point of view, Theoretical Computer Science , 242(2000-07), 29-40
32.  (with H.H. Chern ! H. K. Hwang) Distribution of the number of consecutive records, Random structure and Algorithms , 17(2000-08), 169-196
33.  (with Cheng-Der Fuh) A random perturbation in the games of chances, Studies in Applied Mathematics , 17(2001-08), 207-215
34.  (with Beifang Chen ! Shing-Tung Yau) Graph homotopy and Graham homotopy, Discrete Mathematics , 241(2001-10), 153-170
35.  (with Xiaokai Yang) Endogenous specialization and Endogenous principal-agent relationship, Australian Economic Paper , 41(2002), 15-36
36.  (with Sen-Peng Eu and Shu-Chung Liu) Taylor expansions for Catalan and Motzkin numbers, Advances in Applied Mathematics , 29(2002-10), no. 3, 345-357
37.  (with Edward H. Ip andYuchung J. Wang) Some equivalence results concerning multiplicative lattice decompositions of multivariate densities., J. Multivariate Anal. , 84(2003-02), no. 2, 403-409
38.  (with Yew-Kwang Ng) Comparative Statics without Total Differentiation of the First Order Conditions, Economics Letters , 78(2003-02), 161-166
39.  (with Sen-Peng Eu and Shu-Chung Liu) Dyck paths with peaks avoiding or restricted to a given set., Studies in Applied Mathematics , 111(2003-11), no. 4, 453-465
40.  (with Edward H. Ip and Yuchung J. Wang) Structural decompositions of multivariate distributions with applications in moment and cumulant., J. Multivariate Anal. , 89(2004-04), no. 1, 119-134
41.  (with Sen-Peng Eu and Shu-Chung Liu) Odd or even on plane trees, Discrete Math. , 281(2004-04), 189-196
42.  (with Bo-Yin Yang) A crowning moment for Wiener indices, Studies in Applied Mathematics , 112(2004-05), no. 4, 333-340
43.  (with Bo-Yin Yang) Wiener polynomials of some chemically interesting graphs., International Journal of Quantum Chemistry , 99(2004-08), 80-91
44.  (with Yi Wang) Proof of a conjecture on unimodality, European Journal of Combinatorics , 26(2005-07), 617-627
45.  (with Z.W. Sun) On various restricted sumsets, J. Number Theory , 114(2005-10), 209-220
46.  (with S.P. Eu !T. S. Fu) Refined Chung- Feller Theorems for lattice paths, Journal of Combinatorial Theory (series A) , 112(2005-10), 145-162
47.  (with Weigen Yan and Fuji Zhang) Ordering the complements of trees by the number of maximum matchings, International Journal of Quantum Chemistry , 105(2005-10), 131-141
48.  (with Weigen Yan and Fuji Zhang) On the Matching Polynomials of Graphs with Small Number of cycles of even length, International Journal of Quantum Chemistry , 105(2005-10), 124-130
49.  (with Yi Wang) Polynomials with real zeros and Polya frequency sequences, Journal of Combinatorial Theory (Series A) , 109(2005-11), 63-74
50.  (with Weigen Yan and Fuji Zhang) Graphical condensation of plane graphs: a combinatorial approach, Theoretical Computer Science , 349(2005-12), no. 3, 452-461
51.  (with Weigen Yan) Connections between Wiener index and Matchings, Journal of Mathematical Chemistry , 39(2006-02), 389-399
52.  (with Sen-Peng Eu ! Bo-Yin Yang) Generalized Wiener Indices in Hexagonal Chains, International Journal of Quantum Chemistry , 106(2006-2), no. 2, 426-435
53.  (with Sen-Pern Eu and Shu-Chung. Liu) On the Congruences of Some Combinatorial Numbers, Studies in Applied Mathematics , 116(2006-2), no. 2, 135-144
54.  (with Weigen Yan) A simple proof of Graham and Pollak's theorem, Journal of Combinatorial Theory(Series A) , 113(2006-07), no. 2, 892-893
55.  (with Xiaofeng Guo! D. J. Klein ! Weigen Yan) Hyper Wiener Vector, Wiener Matrix Sequence and Wiener, International Journal of Quantum Chemistry , 106(2006 -07), no. 8, 1756-1761
56.  (with Weigen Yan) On the number of matchings of graphs formed by a graph operation, Series A Mathematics, Science in China , 113(2006-10), 892-893
57.  (with Weigen Yan) Enumeration of subtrees of trees, Theoretical Computer Science , 369(2006-12), no. 2, 256-268
58.  (with Yi Wang) Log-concavity and LC-Positivity, Journal of Combinatorial Theory(Series A) , 114(2007-02), no. 2, 195-210
59.  (with Weigen Yan! Bo-Yin Yang) The Behavior of Wiener Indices and Polynomials of Graphs under Five Graph Operators, Applied Mathematics Letters , 20(2007 -03), no. 3, 290-295
60.  (with Weigen Yan) Replacing Pfaffians and applications, Advances in Applied Mathematics , 39(2007-07), no. 1, 121-140
61.  (with Ivan Gutman! Weigen Yan! Bo-Yin Yang) Generalized Wiener Indices of Zigzagging Pentachains, Journal of Mathematical Chemistry , 42(2007-08), no. 2, 103-117
62.  (with Weigen Yan) The determinants of q-distance matrices of trees and two quantities relating to permutations, Advances in Applied Mathematics , 39(2007-09), no. 3, 311-321
63.  (with Lih-Hsing Hsu and Shu-Chung Liu) Hamiltonicity of hpercubes with a contrait of required and faulty edges, Combinatorial Optimization , 14(2007-10), no. 2-3, 197-204
64.  (with Weigen Yan) On the monomer-dimer problem of some graphs, Studies in Applied Mathematics , 120(2008-05), no. 4, 351-360
65.  (with Weigan Yan and Fuji Zhang) Dimer problem on the cylinder and torus, Physica A , 387(2008-06), no. 24, 6069-6078
67.  (with S.P. Eu and S.C. Liu) Catalan and Motzkin numbers modulo 4 and 8, European Journal of Combinatorics , 29(2008-08), no. 6, 1449-1466
68.  (with Shu-Chung Liu and Jun Ma) Dyck Paths with Peak- and Valley-avoiding Set, Studies in Applied Mathematics , 121(2008-08), no. 3, 263-289
69.  (with Weigen Yan) On the matching polynomial of subdivision graphs, Discrete Applied Mathematics , 157(2009-01), no. 1, 196-200
70.  (with N. Sh. Izmailian) Ising model with mixed boundary conditions: universal amplitude ratios, Nuclear Phys. B , 814(2009-06), no. 3, 573-581
71.  (with Jun Ma) Generalizations of Chung-Feller Theorems I, Bulletin of the Institute of Mathematics,Academia Sinica New Series , 4(2009-09), no. 3, 299-332
72.  (with Ji-Ming Guo and Weigen Yan) On the nullity and the matching number of unicyclic graphs, Linear Algebra and Its Applications , 431(2009-09), no. 8, 1293-1301
73.  (with Hungyung Chang and Jun Ma) Tutte polynomials and G-parking functions, Advances in Applied Mathematics , 44(2010-03), no. 3, 231-242
74.  (with Pierre Bouchard, Hungyung Chang, Jun Ma, and Jean Yeh) Value-Peaks of Permutations, The electronic journal of combinator , 17(2010-03), no. #R46, 0-0
75.  (with Po-Yi Huan and Jun Ma) Cyclic permutation of sequence and uniform partition, The Electronic Journal of Combinatorics , 17(2010-08), no. #117, 0-0
76.  (with Jun Ma) Refinements of (n;m)-Dyck paths, European Journal of Combinatorics (2011-01), no. 32, 92-99
77.  (with Xun-Tuan Su1, Yi Wan) Unimodality problems of multinomial coefficients, The Electronic Journal of Combinatorics, , 18(2011-03), no. #73, 117-0
78.  (with Shu-Chung Liu and Yi Wang) Chung-Feller Property in View of Generating Functions, The Electronic Journal of Combinatorics, , 18(2011-05), no. #104, 0-0
79.  (with Weigen Yan and Fuji Zhang) Dimers belonging to three orientations on plane, Journal of Statistical Physics , 145(2011-12), no. 5, 1343-1356(DOI: 10.1007/s10955-011-0348-y)
80.  (with Jun Ma) Combinatorial interpretations for T_G(1,-1), Journal of Graph Theory , 69(2012-03), 341-348(Article first published online: 9 FEB 2011DOI: 10.1002/jgt.20588)
81.  (with Weigen Yan, Fuzi Zhang) The asymptotic behavior of some indices of iterated line graphs of regular graphs, Discrete Applied Mathematics , 160(2012), 1232-1239
82.  (with X. Lin, S. J. Xu,) Hosoya Polynomials of Circumcoronene Series, MATCH communications in mathematical and in computer chemistry , 69(2013), 755-763
83.  (with Po-Yi Huangand Jun Ma) Non-decreasing k-flaw Preference Sets, Southeast Asian Bulletin of Mathematics , 37(2013), 515-535
84.  (with Po-Yi Huang, Shu-Chung Liu) Congruences of Finite Summations of the Coefficients in certain Generating Functions, The Electronic Journal of Combinatorics , 21(2014-07), no. 2 (p45), 0-0
85.  (with Chen, Xiao-Min; Chang, Xiang-Ke; Sun, Jian-Qing; Hu, Xing-Biao) Three semi-discrete integrable systems related to orthogonal polynomials and their generalized determinant solutions., Nonlinearity , 28(2015), 2279-2306
86.  (with Jun Ma and Hao Shen) Rooted cyclic permutations of lattice paths and uniform partitions, Discret mathematics , 338(2015), 1111-1125
87.  (with Shi-Mei Ma) Stirling permutations, cycle structures of permutations and perfect matchings, Electronic Journal of Combinatorics , 22(4)(2015), 42, 9 pp.-
88.  (with Li Shanhai, Ma Jun) Uniform partition extensions, a generating functions perspective, Science China Mathematics , 58(2015), 2655-2670(doi: 10.1007/s11425-015-5050-0)
89.  (with Ya-Lei Jin, Xiao-Dong Zhang) Laplacian Coefficient, Matching Polynomial and Incidence Energy of of Trees with Described Maximum Degree, JOURNAL OF COMBINATORIAL OPTIMIZATION , 31(2016-04), 1345–1372-
90.  (with Hongchuan Lei , Heping Zhang) Anti-forcing numbers of perfect matchings of graphs, Discrete Applied Mathematics , 202(2016), 95 –105-0
91.  (with Ma jun) Parking functions on nonsingular M-matrices, Linear Algebra and its Applications , 489(2016), 1-14
92.  (with Shi-Mei Ma) Enumeration of permutations by number of alternating descents, DISCRETE MATHEMATICS , 339(2016), no. 4, 1362-1367(DOI : 10.1016/j.disc.2015.12.007)
93.  (with Shi-Mei Ma) The peak statistics on simsun permutations, Electronic_journal_of_combinatorics , 23(2016), no. P2.14
94.  (with Xiang-Ke Chang, Xing-Biao Hu, Hongchuan Lei) Combinatorial proofs of addition formulas, Electronic Journal of Combinatorics , 23(2016-01), no. p 1.8
95.  (with Jun Ma, Shi-Mei Ma, Xu Zhu) The Cycle Descent Statistic on Permutations Electronic Journal of Combinatorics, 23 (2016), no. p 4.20., Electronic Journal of Combinatorics , 23(2016), no. 4, 20-20
96.  (with Lili Mu, Yi Wang) Hankel determinants of linear combinations of consecutive Catalan-like numbers, Discrete Mathematics , 340(2017-09), no. 12, 3097-3103
97.  (with Shi-Mei Ma) Eulerian polynomials, Stirling permutations of the second kind and perfect matchings, Electronic journal of combinatorics , 24(2017-11), no. 4, 27.1-27.18
98.  (with R Xu, X Zhu) List colouring of graphs and generalized Dyck paths, Discrete Mathematics , 341(2018), no. 3, 810-819
99.  (with Jun Ma, Shi-Mei Ma, B-X Zhu) Context-free grammars for several polynomials associated with Eulerian polynomials, The electronic journal of combinatorics , 25(2018), no. 1, 1-31
100.  (with Duh Guan-Huei , Lin Yen-ChiRoger, Ma Shi-Mei) Some statistics on Stirling permutations and Stirling derangements, Discrete Mathematics , 341(2018-07), no. 9, 2478-2484
101.  (with Shi-Mei Ma,Touk Mansour,David G.L.Wang) Several variants of the Dumont differential system and permutation statistics, Science China A,Mathematics, (2018-02)
102.  (with Yen-chi Lin, Shi-Mei Ma) Counting Permutations by Simsun Successions, Taiwanese Journal of Mathematics (2018)