Research Fellow | Yeh, Yeong-Nan

**Contact Information**

- mayeh$\color{red}{@}$math.sinica.edu.tw
- +886 2 2368-5999 ext. 629
- +886 2 2368-9771

**Research Interests**

- Combinatorics
- Mathematical Chemistry

**Education**

- Ph.D. in Mathematics State University of NY at Buffalo (1983-1985)
- M.S. in Mathematics State University of NY at Buffalo (1981-1983)
- B.S. in Mathematics National Taiwan University (1974-1978)

**Links**

**Work Experience**

- Vice director Institute of Mathematics, Academia Sinica, Nankang, Taipei, Taiwan, R.O.C. 2005/9 -2006/4
- 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.

**Awards**

- The special contract research plans, National Science Council, R.O.C., 2018~2020
- Outstanding Research Award, Academia Sinica, R.O.C., 2010~2014,2016~2017,2019
- 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

**Research Descriptions**

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.

**Selected Publications**

- (with SHI-MEI MA, JUN MA AND ROBERTA R. ZHOU) "JACOBIAN ELLIPTIC FUNCTIONS AND A FAMILY OF BIVARIATE PEAK POLYNOMIALS"
,
*European Journal of Combinatorics*, 2021-05. - (with Shi-Mei Ma, Jun Ma, Jean Yeh,) "The 1/k-Eulerian polynomials of type B"
,
*The Electronic Journal of Combinatorics*, 2020-08. - (with Hayoung Choi , Seonguk Yoo) "Catalan-like number sequences and Hausdorff moment sequences"
,
*Discrete Mathematics*, 343 (5), 111808-, 2020-05. - (with Suijie Wang, Fengwei Zhou,) "Linear Bounds on Characteristic Polynomials of Matroids"
,
*Mathematical Proceedings of the Cambridge Philosophical Society*, 2020-05. - (with Ma, Shi-Mei; Ma, Jun) "David-Barton type identities and alternating run polynomials"
,
*Advances in Applied Mathematics*, 114, 107978-, 2020-03. - (with Shi-Mei Ma,Touk Mansour,David G.L.Wang) "Several variants of the Dumont differential system and permutation statistics"
,
*Science China A,Mathematics,*, 62 (10), 2033-2052, 2019-10. - (with Jun Ma, Ting-Wei Chao, Shi-Mei Ma) "1/k-Eulerian polynomials and k-inversion sequences"
,
*The Electronic Journal of Combinatorics*, 2019-08. - (with Lin Yen-Chi Roger, Ma, Shi-Mei) "Counting permutations by simsun successions."
,
*Taiwanese J. Math.*, 23 (3), 515-527, 2019-06. - (with Ma, Shi-Mei, Ma, Jun) "γ-POSITIVITY AND PARTIAL γ-POSITIVITY OF DESCENT-TYPE POLYNOMIALS"
,
*J. Combin. Theory Ser. A*, 167, 257-293, 2019-06. - (with Bao-Xuan Zhu;Qinglin Lu) "Context-free grammars, generating functions and combinatorial arrays"
,
*European Journal of Combinatorics*, 78, 236-255, 2019-05. - (with Jun Ma, Shi-Mei Ma) "The ascent-plateau statistics on Stirling permutations"
,
*Electronic Journal of Combinatorics,*, 26 (2), 2019-04. - (with Jiang, Yiting; Der-Fen Liu, Daphne; Zhu, Xuding) "Colouring of generalized signed triangle-free planar graphs"
,
*Discrete Math.*, 342 (3), 836-843, 2019. - (with Ma, Shi-Mei; Ma, Jun) "On certain combinatorial expansions of the Legendre-Stirling numbers"
,
*Electron. J. Combin.*, 25 (4), 57-66, 2018-12. - (with Duh Guan-Huei , Lin Yen-ChiRoger, Ma Shi-Mei) "Some statistics on Stirling permutations and Stirling derangements"
,
*Discrete Mathematics*, 341 (9), 2478-2484, 2018-09. - (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 (1), 1-31, 2018. - (with R Xu, X Zhu) "List colouring of graphs and generalized Dyck paths"
,
*Discrete Mathematics*, 341 (3), 810-819, 2018. - (with Shi-Mei Ma) "Eulerian polynomials, Stirling permutations of the second kind and perfect matchings"
,
*Electronic journal of combinatorics*, 24 (4), 27.1-27.18, 2017-11. - (with Lili Mu, Yi Wang) "Hankel determinants of linear combinations of consecutive Catalan-like numbers"
,
*Discrete Mathematics*, 340 (12), 3097-3103, 2017-09. - (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, 1345–1372-, 2016-04. - (with Xiang-Ke Chang, Xing-Biao Hu, Hongchuan Lei) "Combinatorial proofs of addition formulas"
,
*Electronic Journal of Combinatorics*, 23 (p 1.8), 2016-01. - (with Jun Ma, Shi-Mei Ma, Xu Zhu) "The Cycle Descent Statistic on Permutations"
,
*Electronic Journal of Combinatorics*, 23 (4), 20-20, 2016. - (with Shi-Mei Ma) "The peak statistics on simsun permutations"
,
*Electronic_journal_of_combinatorics*, 23 (P2.14), 2016. - (with Shi-Mei Ma) "Enumeration of permutations by number of alternating descents"
,
*DISCRETE MATHEMATICS*, 339 (4), 1362-1367, 2016. (DOI : 10.1016/j.disc.2015.12.007) - (with Ma jun) "Parking functions on nonsingular M-matrices"
,
*Linear Algebra and its Applications*, 489, 1-14, 2016. - (with Hongchuan Lei , Heping Zhang) "Anti-forcing numbers of perfect matchings of graphs"
,
*Discrete Applied Mathematics*, 202, 95 –105-0, 2016. - (with Shi-Mei Ma) "Stirling permutations, cycle structures of permutations and perfect matchings"
,
*Electronic Journal of Combinatorics*, 22(4), 42, 9 pp.-, 2015. - (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, 2279-2306, 2015. - (with Li Shanhai, Ma Jun) "Uniform partition extensions, a generating functions perspective"
,
*Science China Mathematics*, 58, 2655-2670, 2015. (doi: 10.1007/s11425-015-5050-0) - (with Jun Ma and Hao Shen) "Rooted cyclic permutations of lattice paths and uniform partitions"
,
*Discret mathematics*, 338, 1111-1125, 2015. - (with Po-Yi Huang, Shu-Chung Liu) "Congruences of Finite Summations of the Coefficients in certain Generating Functions"
,
*The Electronic Journal of Combinatorics*, 21 (2 (p45)), 2014-07. - (with X. Lin, S. J. Xu,) "Hosoya Polynomials of Circumcoronene Series"
,
*MATCH communications in mathematical and in computer chemistry*, 69, 755-763, 2013. - (with Po-Yi Huangand Jun Ma) "Non-decreasing k-flaw Preference Sets"
,
*Southeast Asian Bulletin of Mathematics*, 37, 515-535, 2013. - (with Jun Ma) "Combinatorial interpretations for T_G(1,-1)"
,
*Journal of Graph Theory*, 69, 341-348, 2012-03. (Article first published online: 9 FEB 2011DOI: 10.1002/jgt.20588) - (with Weigen Yan, Fuzi Zhang) "The asymptotic behavior of some indices of iterated line graphs of regular graphs"
,
*Discrete Applied Mathematics*, 160, 1232-1239, 2012. - (with Weigen Yan and Fuji Zhang) "Dimers belonging to three orientations on plane"
,
*Journal of Statistical Physics*, 145 (5), 1343-1356, 2011-12. (DOI: 10.1007/s10955-011-0348-y) - (with Shu-Chung Liu and Yi Wang) "Chung-Feller Property in View of Generating Functions"
,
*The Electronic Journal of Combinatorics,*, 18 (#104), 2011-05. - (with Xun-Tuan Su1, Yi Wan) "Unimodality problems of multinomial coefficients"
,
*The Electronic Journal of Combinatorics,*, 18 (#73), 117-0, 2011-03. - (with Jun Ma) "Refinements of (n;m)-Dyck paths"
,
*European Journal of Combinatorics*(32), 92-99, 2011-01. - (with Po-Yi Huan and Jun Ma) "Cyclic permutation of sequence and uniform partition"
,
*The Electronic Journal of Combinatorics*, 17 (#117), 2010-08. - (with Pierre Bouchard, Hungyung Chang, Jun Ma, and Jean Yeh) "Value-Peaks of Permutations"
,
*The electronic journal of combinator*, 17 (#R46), 2010-03. - (with Hungyung Chang and Jun Ma) "Tutte polynomials and G-parking functions"
,
*Advances in Applied Mathematics*, 44 (3), 231-242, 2010-03. - (with Ji-Ming Guo and Weigen Yan) "On the nullity and the matching number of unicyclic graphs"
,
*Linear Algebra and Its Applications*, 431 (8), 1293-1301, 2009-09. - (with Jun Ma) "Generalizations of Chung-Feller Theorems I"
,
*Bulletin of the Institute of Mathematics,Academia Sinica New Series*, 4 (3), 299-332, 2009-09. - (with N. Sh. Izmailian) "Ising model with mixed boundary conditions: universal amplitude ratios"
,
*Nuclear Phys. B*, 814 (3), 573-581, 2009-06. - (with Weigen Yan) "On the matching polynomial of subdivision graphs"
,
*Discrete Applied Mathematics*, 157 (1), 196-200, 2009-01. - (with Shu-Chung Liu and Jun Ma) "Dyck Paths with Peak- and Valley-avoiding Set"
,
*Studies in Applied Mathematics*, 121 (3), 263-289, 2008-08. - (with S.P. Eu and S.C. Liu) "Catalan and Motzkin numbers modulo 4 and 8"
,
*European Journal of Combinatorics*, 29 (6), 1449-1466, 2008-08. - (with Yi Wang) "A CLASS OF LYM ORDERS IN DIVISOR LATTICES"
,
*TAIWANESE JOURNAL OF MATHEMATICS*, 12 (4), 991-996, 2008-07. - (with Weigan Yan and Fuji Zhang) "Dimer problem on the cylinder and torus"
,
*Physica A*, 387 (24), 6069-6078, 2008-06. - (with Weigen Yan) "On the monomer-dimer problem of some graphs"
,
*Studies in Applied Mathematics*, 120 (4), 351-360, 2008-05. - (with Lih-Hsing Hsu and Shu-Chung Liu) "Hamiltonicity of hpercubes with a contrait of required and faulty edges"
,
*Combinatorial Optimization*, 14 (2-3), 197-204, 2007-10. - (with Weigen Yan) "The determinants of q-distance matrices of trees and two quantities relating to permutations"
,
*Advances in Applied Mathematics*, 39 (3), 311-321, 2007-09. - (with Ivan Gutman! Weigen Yan! Bo-Yin Yang) "Generalized Wiener Indices of Zigzagging Pentachains"
,
*Journal of Mathematical Chemistry*, 42 (2), 103-117, 2007-08. - (with Weigen Yan) "Replacing Pfaffians and applications"
,
*Advances in Applied Mathematics*, 39 (1), 121-140, 2007-07. - (with Yi Wang) "Log-concavity and LC-Positivity"
,
*Journal of Combinatorial Theory(Series A)*, 114 (2), 195-210, 2007-02. - (with Weigen Yan! Bo-Yin Yang) "The Behavior of Wiener Indices and Polynomials of Graphs under Five Graph Operators"
,
*Applied Mathematics Letters*, 20 (3), 290-295, 2007 -03. - (with Sen-Peng Eu ! Bo-Yin Yang) "Generalized Wiener Indices in Hexagonal Chains"
,
*International Journal of Quantum Chemistry*, 106 (2), 426-435, 2006-2. - (with Sen-Pern Eu and Shu-Chung. Liu) "On the Congruences of Some Combinatorial Numbers"
,
*Studies in Applied Mathematics*, 116 (2), 135-144, 2006-2. - (with Weigen Yan) "Enumeration of subtrees of trees"
,
*Theoretical Computer Science*, 369 (2), 256-268, 2006-12. - (with Weigen Yan) "On the number of matchings of graphs formed by a graph operation"
,
*Series A Mathematics, Science in China*, 113, 892-893, 2006-10. - (with Weigen Yan) "A simple proof of Graham and Pollak's theorem"
,
*Journal of Combinatorial Theory(Series A)*, 113 (2), 892-893, 2006-07. - (with Weigen Yan) "Connections between Wiener index and Matchings"
,
*Journal of Mathematical Chemistry*, 39, 389-399, 2006-02. - (with Xiaofeng Guo! D. J. Klein ! Weigen Yan) "Hyper Wiener Vector, Wiener Matrix Sequence and Wiener"
,
*International Journal of Quantum Chemistry*, 106 (8), 1756-1761, 2006 -07. - (with Weigen Yan and Fuji Zhang) "Graphical condensation of plane graphs: a combinatorial approach"
,
*Theoretical Computer Science*, 349 (3), 452-461, 2005-12. - (with Yi Wang) "Polynomials with real zeros and Polya frequency sequences"
,
*Journal of Combinatorial Theory (Series A)*, 109, 63-74, 2005-11. - (with Weigen Yan and Fuji Zhang) "Ordering the complements of trees by the number of maximum matchings"
,
*International Journal of Quantum Chemistry*, 105, 131-141, 2005-10. - (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, 124-130, 2005-10. - (with Z.W. Sun) "On various restricted sumsets"
,
*J. Number Theory*, 114, 209-220, 2005-10. - (with S.P. Eu !T. S. Fu) "Refined Chung- Feller Theorems for lattice paths"
,
*Journal of Combinatorial Theory (series A)*, 112, 145-162, 2005-10. - (with Yi Wang) "Proof of a conjecture on unimodality"
,
*European Journal of Combinatorics*, 26, 617-627, 2005-07. - (with Bo-Yin Yang) "Wiener polynomials of some chemically interesting graphs."
,
*International Journal of Quantum Chemistry*, 99, 80-91, 2004-08. - (with Bo-Yin Yang) "A crowning moment for Wiener indices"
,
*Studies in Applied Mathematics*, 112 (4), 333-340, 2004-05. - (with Sen-Peng Eu and Shu-Chung Liu) "Odd or even on plane trees"
,
*Discrete Math.*, 281, 189-196, 2004-04. - (with Edward H. Ip and Yuchung J. Wang) "Structural decompositions of multivariate distributions with applications in moment and cumulant."
,
*J. Multivariate Anal.*, 89 (1), 119-134, 2004-04. - (with Sen-Peng Eu and Shu-Chung Liu) "Dyck paths with peaks avoiding or restricted to a given set."
,
*Studies in Applied Mathematics*, 111 (4), 453-465, 2003-11. - (with Yew-Kwang Ng) "Comparative Statics without Total Differentiation of the First Order Conditions"
,
*Economics Letters*, 78, 161-166, 2003-02. - (with Edward H. Ip andYuchung J. Wang) "Some equivalence results concerning multiplicative lattice decompositions of multivariate densities."
,
*J. Multivariate Anal.*, 84 (2), 403-409, 2003-02. - (with Sen-Peng Eu and Shu-Chung Liu) "Taylor expansions for Catalan and Motzkin numbers"
,
*Advances in Applied Mathematics*, 29 (3), 345-357, 2002-10. - (with Xiaokai Yang) "Endogenous specialization and Endogenous principal-agent relationship"
,
*Australian Economic Paper*, 41, 15-36, 2002. - (with Beifang Chen ! Shing-Tung Yau) "Graph homotopy and Graham homotopy"
,
*Discrete Mathematics*, 241, 153-170, 2001-10. - (with Cheng-Der Fuh) "A random perturbation in the games of chances"
,
*Studies in Applied Mathematics*, 17, 207-215, 2001-08. - (with H.H. Chern ! H. K. Hwang) "Distribution of the number of consecutive records"
,
*Random structure and Algorithms*, 17, 169-196, 2000-08. - (with H. K. Hwang ! B. Y. Yang) "Presorting algorithms: an average-case point of view"
,
*Theoretical Computer Science*, 242, 29-40, 2000-07. - (with Li-Da Tong ! S.C. Liu) "The tree with the minimum Wiener Number, International"
,
*Journal of Quantum Chemistry*, 78, 331-340, 2000-06. - (with H. K. Hwang) "Measures of distinctness for random partitions and compositions of an integer"
,
*Advances in Applied Mathematics*, 19, 378-414, 1997-10. - (with S. C. Chang) "The cardinality of the collection of maximum independent sets of a graph"
,
*Advances in Applied Mathematics*, 18, 286-299, 1997-04. - (with W. Huang and B. Y. Yang) "From ternary strings to wiener indices of benezoid chains"
,
*Discrete Applied Mathematics*, 73, 113-131, 1997-03. - (with B. Sagan and P. Zhang) "The wiener polynomial of a graph"
,
*International Journal of Quantum Chemistry*, 60, 959-969, 1996-12. - (with I. Gutman and Chin-Mei Fu) "Graph transformations which preserve the multiplicity of an eigenvalue"
,
*Discrete Applied Mathematics*, 67, 221-228, 1996-05. - (with Y. W. Huang and B. Y. Yang) "Wiener index of hexagonal carpets - From hexes to square grids"
,
*Southeast Asian Bulletin of Mathematics*, 20, 81-102, 1996. - "A remarkable endofunction involving compositions"
,
*Studies in Applied Mathematics*, 95, 419-432, 1995-11. - (with B. Gan) "The Nim-like game and dynamic recurrence relations"
,
*Studies in Applied Mathematics*, 95, 213-228, 1995-08. - (with I. Gessel and B. Sagan) "Enumeration of trees by inversions"
,
*Journal of Graph Theory*, 19, 435-459, 1995-07. - (with W. Y. C. Chen and K. W. Lih) "Cyclic tableaux and symmetric functions"
,
*Studies in Applied Mathematics*, 94, 327-339, 1995-04. - "(with B. Y. Yang) Zigging and zagging pentachains"
,
*Advances in Applied Mathematics*, 16, 72-94, 1995-03. - (with B. Y. Yang) "Chains of motley gems and their wiener indices"
,
*Proceedings of Tainan-Moscaw workshop,Tainan,Walter de Gruyter*, 1995. - (with I. Gutman) "On the sum of all distances in bipartite graphs"
,
*Mathematica Slovaca*, 45, 327-334, 1995. - (with R. Servedio) "A bijective proof on circular compositions"
,
*Bull. Inst. Math. , Academia Sinica*, 23, 283-293, 1995. - (with I. Gutman) "On the sum of all distances in composite graphs"
,
*Discrete Mathematics*, 135, 359-365, 1994-12. - "The generating polynomial and Euler characteristic of intersection graphs"
,
*Discrete Mathematics*, 131, 325-333, 1994-08. - (with B. Chen) "Some explanations of the Dobinski's formula"
,
*Studies in Applied Mathematics*, 92, 191-199, 1994-07. - (with B. Sagan and G. Ziegler) "Maxmizing mobius functions on subsets of boolean algebras"
,
*Discrete Mathematics*, 126, 293-311, 1994-03. - (with A. Ivashchenko) "Minimal graph of a torus, a projective plane and spheres. Some properties of minimal graphs of homotopy class"
,
*Discrete Mathematics*, 126, 171-178, 1994-03. - (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, 651-661, 1993-08. - (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, 105-116, 1992-01. - (with F. Bergeron) "The factoriality of the ring of S-species"
,
*Journal of combinatorial Theory (series A)*, 55, 194-203, 1990-11. - (with J. Labelle) "Generalized Dyck paths"
,
*Discrete Mathematics*, 82, 1-6, 1990-05. - (with J. Labelle) "Combinatorial proof of some limit formulas involving orthogonal polynomials"
,
*Discrete Mathematics*, 79, 77-93, 1990-01. - (with J. Labelle) "Dyck paths of knight moves"
,
*Discrete Applied Mathematics*, 24, 213-221, 1989-08. - (with J. Labelle) "The relations between permutation groups and combinatorics species"
,
*Journal of Combinatorial Theory (series A)*, 50, 269-284, 1989-03. - (with J. Labelle) "The combinatorics of Laguerre, Charlier and Hermite polynomials revisited"
,
*Studies in Applied Mathematics*, 80 (1), 25-36, 1989-02. - (with Labelle J.) "A combinatorial Model for hahn polynomials" , 1989.
- (with J. Labelle) "Some combinatorics of the hypergeometric series"
,
*European Journal of Combinatorics*, 6, 593-605, 1988-11. - "The calculus of virtual species an K-species"
,
*Lecture Notes in Mathematics, Springer Verlag*, 1234, 351-369, 1986.

Director & Deputy Director