Retired Research Fellow | Chou, Wun-Seng

**Contact Information**

- macws$\color{red}{@}$math.sinica.edu.tw
- +886 2 2368-5999 ext. 716
- +886 2 2368-9771

**Research Interests**

- Discrete Mathematics
- Number Theory

**Education**

- Ph.D. Pennsylvania State University (1990)
- Southern Illinois University (1984–1986)
- M.S. Fu-Jen Catholic University (1976)
- B.S. Fu-Jen Catholic University (1974)

**Links**

**Work Experience**

- Professor Department of Mathematical Sciences, National Chengchi University 2009/8
- Deputy Director Institute of Mathematics, Academia Sinica 2009/4 -2011/3
- Director Mathematical Research Promotion Center 2005 - 2007
- Director Mathematical Research Promotion Center 2005 - 2007
- Deputy Director Institute of Mathematics, Academia Sinica 2000/8 - 2004/12
- Supervisor the mathematics library, Academia Sinica 1999 - 2000
- Research Fellow 1999
- Associate Research Fellow 1990 - 1999
- Instructor Chinese Culture University 1978 - 1984

**Research Descriptions**

Wun-Seng Chou received his B.S. and M.S. from the Department of Mathematics, Fu-Jen Catholic University. After his military service, he taught in college level for 6 years. He went to the United States in 1984. He studied in the Southern Illinois University-Carbondale for 2 years and then transferred to the Pennsylvania State University. He received his Ph.D. in mathematics from the PSU in 1990. Since then, he joined the Institute of Mathematica, Academia Sinica as an Research Fellow. His major research interest is the finite field theory and its applications.

**Selected Publications**

- (with A. Blokhuis, X. Cao and X.-D. Hou) "On the Roots of Certain Dickson Polynomials"
,
*J. Number Theory*, 186, 229-246, 2018-07. - (with Tian-Xiao He and Peter J.-S. Shiue) "On the Primality of the Generalized Fuss-Catalan Numbers"
,
*J. Integer Sequences*, 21, 18.2.1-, 2018. - (with X. Cao and X. Zhang) "More constructions of near optimal codebooks associated with binary sequences"
,
*Advances in Mathematics of Communications*, 11 (1), 187-202, 2017-02. - (with X. Cao, J. Gu) "On the number of solutions of certain diagonal equations over finite fields"
,
*FINITE FIELDS AND THEIR APPLICATIONS*, 42, 225-252, 2016. - (with Cao X.) "More Constructions of Approximately Mutually Unbiased Bases"
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*Bulletin of the Australian Mathematical Society*, 93, 211-222, 2016. - (with Hsu L. C.) "An Extension of Fleck-type M$\ddot{\mbox{o}}$bius Function and Inversion"
,
*International Journal Of Number Theory*, 11 (6), 1807-1819, 2015. - (with He T.-X., Shiue P. J.-S.) "Enumeration problems for a linear congruence equation"
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*Taiwanese Journal of Mathematics*, 18 (1), 265-275, 2014-02. - (with He T.-X.) "On the construction of number sequence identities"
,
*J. Concrete and Appl. Math.*, 11, 277-291, 2013. - (with J. Gomez-Calderon, G. L. Mullen, D. Panario, D. Thomson) "Subfield value sets of polynomials over finite fields"
,
*Functiones et Approximatio Commentarii Mathematici*, 48 (1), 147-165, 2013. - (with G.L. Mullen! B. Wassermann) "On the number of solutions of equations of Dickson polynomials over finite fields, NSC94-2115-M-001-019"
,
*Taiwanese Journal of Mathematics*, 12, 917-931, 2008. - (with B.-S. Du ! P.J.-S.Shiue) "A note on circulant transition matrices in Markov chains, NSC94-2115-M-001-019"
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*Linear Algebra and Its Applications*, 429, 1699-1704, 2008. - (with L.C.Hsu!P.J.-S.Shiue) "On a class of combinatorial sums involving generalized factorials, doi:10.1155/2007/12604"
,
*Int. J. Math. & Math. Sciences*, 2007. - (with P. J.-S. Shiue) "Periodic aspects of sequences generated by two special mappings"
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*Taiwanese J. Math.*, 10 (4), 829-836, 2006. - (with L. C. Hsu ! P. J.-S. Shiue) "Application of Faa di Bruno's formula in characterization of inverse relations"
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*J. Comput. Applied Math*, 190, 151-169, 2006. - (with Y. Chang and P. J.-S. Shiue) "On the number of primitive polynomials over finite fields"
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*Finite Fields & Their Appls.*, 11, 156-163, 2005. - (with I. E. Shparlinski) "On the cycle structure of repeated exponentiation modulo a prime. NSC92-2115-M-001-026"
,
*J. Number Theory*, 107, 345-356, 2004. - (with T. C. Brown and P. J.-S. Shiue) "On the partition function of a finite set"
,
*Australasian J. Comb.*, 27, 193-204, 2003. - (with H. Niederreiter) "Monomials and binomials over finite fields as $\scr R$-orthomorphisms. NSC88-2115-M-001-002"
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*Publ. Math. Debcreen*, 61, 511-521, 2002. - (with S. D. Cohen) "Primitive elements with zero traces. NSC88-2115-M-001-002"
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*Finite Field & Their Appls.*, 7, 125-141, 2001. - (with P. J.-S. Shiue) "crossings on the 2-D torus"
,
*ARS Combinatorica*, 54, 29-31, 2000. - (with S. D. Cohen) "Polynomial distribution and sequences of irreducible polynomoials over finite finite fields"
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*J. Number Theory*, 75, 145-159, 1999. - (with J.-M. Ku and P. J.-S. Shiue) "On crossings of hyperplanes on the n-D torus"
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*J. Algebra*, 192, 43-54, 1997. - "The factorization of Dickson polynomials over finite fields"
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*Finite Fields & Their Appls.*, 3, 84-96, 1997. - (with H. Niederreiter) "On the lattice test for inversive congruential pseudorandom numbers, Monte Carlo & Quasi-Monte Carlo Methods in Scientific Computing (Las Vegas, 1994), Lecture Notes in Statistics, vol.~106, pp.~186--197, Springer-Verlag, New York, 1995" , 1995.
- "The period lengths of inversive congruential recursions"
,
*Acta Arith.*, 73, 325-341, 1995. - "On inversive maximal period polynomials over finite fields"
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*Applicable Algebra in Engrg. Comm. Comp.*, 6, 245-250, 1995. - "The period lengths of inversive pseudorandom vector generations"
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*Finite Fields & Their Appls.*, 1, 126-132, 1995. - (with Y. Manoussakis, O. Megalakaki, M. Spylatos, and Zs. Tuza) "Paths through fixed vertices in edge-colored graphs"
,
*Math. Inf. Sci. Hum.*, 49-58, 1994. - (with P. J.-S. Shiue) "A note on circular permutations"
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*J. Comb. Math. Combl. Comp.*, 16, 165-170, 1994. - "Set-complete mappings on finite fields, Finite Fields, Coding Theory, and Advances in Communications and Computing (Las Vegas, 1991), Lecture Notes in Pure and Appl. Math., vol. 141, pp. 33--41, Dekker, New York, 1993." , 1993.
- (with G. L. Mullen) "Generating linear spans over finite fields"
,
*Acta Arith.*, 61, 183-191, 1992. - "Formulas for counting chains in multisets"
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*Utilitas Math.*, 40, 3-12, 1991. - (with H. Bowman and P. J.-S. Shiue) "A matrix method for solving the postage stamps problem"
,
*Missouri J. Math. Sciences*, 2, 70-76, 1991. - "Permutation Polynomials on Finite Fields and Combinatorial Applications"
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*Ph.D. thesis, Penn. State University*, 1990. - (with G. L. Mullen, P. J.-S. Shiue, and Q. Sun) "Pairs of primitive elements modulo $p^l$"
,
*J. Sichuan Univ. Natural Science*, 26, 189-195, 1989. - (with J. Gomez-Calderon and G. L. Mullen) "Value sets of Dickson polynomials over finite fields"
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*J. Number Theory*, 30, 334-344, 1988. - "Binomial permutations of finite fields"
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*Bull. Austral. Math. Soc.*, 38, 325-327, 1988.

Director & Deputy Director