王軍

社徠會兼職

全國組合數學研究會常務理事，副理事長；美國數學會會員

研究領域（研究課題）

主要的研究領域是“組合數學”，包括組合分析、組合計數、偏序集上的組合、字上的組合以及組合數學中的代數與數論方法等課題。

（1）主持“組合數學中的數論方法”（1992.1-1994.10），國家自然科學基金

（青年基金）項目

（2）參加“組合數學的方法與理論”（1993.1-1997.12），國家自然科學基金八五重點項目

（3）參加“組合數學的理論和方法”（1999.1-2003.12），國家自然科學基金九五

重點項目

（4）主持“偏序集的組合理論及應用”（1998.1-2000.12），遼寧省自然科學基金項

目

（5）主持“組合數學及在符號動力學、分子生物學中的應用”（1999.1-2000.12）,

《高等學校骨幹教師資助計劃》項目

（6）主持“代數組合學的幾何理論”（2002.1-2005.12), 國家自然科學基金兩個基地項目

（7）主持“偏序集上的組合學與計數-枚舉組合學”（2005.1-2007.12），國家自然科學基金面上項目

碩博研究方向

組合數學

出版著作和論文

主要論文

1. 有限域中的第二型本原根的階及其范數，數學學報，34 (1991), No.1, 1-6.

2. 模奇數的廣義分圓方程的可約性，科學通報，36 (1991), No.18, 1365-1367(中

文版）. Chinese Science Bulletin，37(1992), No.4, 281-284 （英文版）.

3. On the Jacobi sums modulo Pn, J. Number Theory， 39 (1991), 50-64.

4. Goldbach's problem in the ring Mn(Z), Amer. Math. Monthly，99 (1992), No.9, 856-857.

5. On the Poincare series for diagonal forms, Proc. Amer. Math. Soc.， 116 (1992), No.3, 607-611.

6. On the Poincare series for diagonal forms over algebraic number fields,Acta Arithmetica，63 (1993), No.2, 97-101.

7. Reduced phi-partitions of positive integers, Fibonacci Quarterly，31 (1993), No.4, 365-369.

8. On the Jacobi sums for finite commutative rings with identity, J. Number Theory, 48 (1994), No.3, 284-290.

9. On the k-th derivative sequences of Fibonacci and Lucas polynomials, Fibonacci Quarterly,33 (1995), No.2, 174-178.

10. A generalization of Menon's identity with respect to a set of polynomials (with Pentti Haukkanen). Portugal. Math., 53 (1996), No.3, 331-337.

11. High degree analogs of Menon's identity (with P. Haukkanen), Indian J. Math., 39 (1997), No.1, 37-42.

12. On Smith's determinant (with Pentti Haukkanen and Juha Sillanpaa), Linear Algebra Appl., 258 (1997), 251-269.

13. Quasi-abelian Cayley graphs and Parsons graphs (with Mingyao Xu), European J. Combin., 18 (1997), 597-600.

14. Euler's totient function and Ramanujan's sum in a poset-theoreticsetting (with P. Haukkanen).Discussiones Mathematicae-Algebra and Stochastic Methods, 17 (1997), 79-87.

15. Proof of a conjecture on the Sperner property of the subgroup lattice of an abelian p-group, Annals of Combin., 2 (1998), 85-101.

16. Minimum cutsets for an element of a subspace lattice over a finite vector space (with H. Feng),Order, 14 (1997-1998), 145-151.

17. Some Mobius-type Functions and Inversions Constructed via Difference Operators (with L.C. Hsu),Tamkang J. Math., 29 (1998), No.2, 89-99.

18. On quasi-invariant elements in a lattice (with H. Feng), Algebra Universalis , 40 (1998), 447-451.

19. Quotient sets and subset-subspace analogy, Advances in Applied Mathematics, 23 (1999), 333-339.

20. 交換 p-群的子群格的強Sperner性質 (with 王毅），中國科學（A輯），30 (2000），232-240; 43 (2000), No.7,693-702 (英文版).

21. Systems of Linear Congruences with Individual Moduli (with David C. Torney), Linear Algebra Appl., 318 (2000), 195-208.

22. Adjacency Relation and Parity Distribution of Lexical Words in Discrete Dynamical Systems (with William Y.C. Chen, James D. Louck), J. Combin. Theory, Ser.A, 91 (2000), 476-508.

23. Some Properties of the (q,h)-binomial Coefficients (with Z.Z. Zhang), J. Physics A: Math. Gen.,33 (2000), 7653-7658.

24. 研究偏序集的Sperner性質的一個新方法, 大連理工大學學報, 40 (2000), 增刊1，5-7.

25. On a certain kind of generalized number-theoretic Mobius function (with T.C. Brown, L.C. Hsu and P. Shiue), Math. Scientist, 25 (2000), 1-6.

26. Decompositions of Necklaces (with William Y.C. Chen), Annals of Combin., 5 (2001), no. 3-4, 271--283.

27. Normalized Matching Property of the Subgroup Lattice of an Abelian p-Group, Discrete Math., 257 (2002), no.2-3, 559-574.

28. Characteristic Sequences for DNA Primary Sequence (with Ping-an He), J. Chem. Infor. Comp. Sci., 42 (2002), 1080-1085.

29. Numerical Characterization of DNA Primary Sequence (with Ping-an He), Internet Electronic Journal of Molecular Design, 1 (2002), No.12, 668-674.

30. Artificial Neural Network Method for Predicting Protein Coding Genes in the Yeast Genome Based on the n-shade Sequences (with Chun Li), Internet Electronic Journal of Molecular Design, 2 (2003), 527-538.

31. On the Hankel Matrix of Derangement Polynomials (with Z.Z. Zhang), Indian J. Pure and Appl. Math., 34 (2003), no.4, 625-629.

32. Numerical characterization and similarity analysis of DNA sequences based on 2-D graphical representation of the characteristic sequences (with Chun Li), Combinatorial Chemistry & High Throughput Screening, 6 (2003), no.8, 795-799.

33. On a 3-D representation of DNA primary sequences (with Chun Li), Combinatorial Chemistry & High Throughput Screening, 7 (2004), no.1, 23-27.

34. On Extensions of Calkin's Binomial Identities (with Zhizheng Zhang), Discrete Math., 274 (2004), 331-342.

35. Some Properties for DNA curve (with Ping-an He), J. Physics A: Math. Gen., 37 (2004), No.42, 7135-7142.

36. Construction of Sturmian Sequences (with Kebo Lu), J. Physics A: Math. Gen., 38 (2005), No.42, 2891-2897.

37. Relative Entropy of DNA and its Application (with Chun Li), Physica A, 347 (2005), 465-471.

38. New Invariant of DNA Sequences (with Chun Li), J. Chem. Infor. Model., 45 (2005), 115-120.

39. Two Operator Identities and Their Applications to Terminating Basic Hypergeometric Series and q-integrals (with Zhizheng Zhang), J. Math. Anal. Appl., 312 (2005), 653-665.

40. Bernoulli matrix and its algebraic properties (with Zhizheng Zhang), Discrete Appl. Math., 154 (2006), 1622–1632.

41. Recognition of protein coding genes in the yeast genome based on the relative entropy of DNA (with Chun Li and Nadia Helal), Combinatorial Chemistry & High Throughput Screening, 9 (2006), No.1, 49-54.

42. Characterization and similarity analysis of DNA sequences grounded on a 2-D graphical representation (with Yi Zhang), Chemical Physics Letters, 423 (2006), No.1-3, 50-53.

43. Characterization and similarity analysis of DNA sequences based on mutually direct-complementary triplets (with Yi Zhang), Chemical Physics Letters, 425 (2006), Issues 4-6, 324-328.

44. On the Set of Reduced Phi-Partitions of a Positive Integer, (with Xin Wang), Fibonacci Quarterly, 44.2 (2006), 98-102.

45. Directed graphs of DNA sequences and their numerical characterization (with Chun Li and Nannan Tang), J. Theoret. Biology, 241 (2006), 173-177.

46. A naturally logical representation for DNA primary sequences (with Chun Li), Combinatorial Chemistry & High Throughput Screening, 10 (2007), No.4, 277-281.

47. k-Step Fibonacci Sequence Modulo m (with Kebo Lu), Utilitas Mathematica,71 (2006), 169-178.

48. Normalized Matching Property of a Class of Subspace Lattices (with Huajun Zhang), Taiwanese Journal of Mathematics, 11, No.1 (2007), 43-50.

49. Cutset condition for geometric lattices (with Jun Wu), Order, 23 (2006), 333-338.

50. Erdos-Ko-Rado-Type Theorems for Colored Sets (with Yushuang Li), Electron. J. Combin. 14 (1) (2007), R1.

51. Similarity analysis of DNA sequences based on the generalized LZ

complexity of (0,1)-sequences (with Chun Li), Journal of Mathematical Chemistry, to appear. (DOI 10.1007/s10910-006-9176-8)

52. Volatilities of Codons and Its Application in Similarity Analysis of Biological Sequences (with Yi Zhang), Journal of Mathematical Chemistry, to appear. (DOI:10.1007/s10910-007-9235-9)

53. On (a,d)-Antimagic Labelings of Generalized Petersen Graphs P(n,2) (with Jirimutu), Ars Combinatoria, to appear.

54. A Sequence Representation of the Dyck Path Poset (with Yushuang Li), Ars Combinatorics, to appear.

55. New proof of a combinatorial identity on Stirling numbers of the second kind (with Caihuan Zhang), Utilitas Mathematica, to appear.

56. A condition for modular lattices (with Jun Wu), Algebra Univeralis, to appear.

57. Combinatorics on Words in Symbolic Dynamics: The Quadratic Map (with Wanji Dai, Kebo Lu), Acta Mathematica Sinica, to appear.

58. Combinatorics on Words in Symbolic Dynamics: The Antisymmetric cubic Map (with Wanji Dai, Kebo Lu), Acta Mathematica Sinica, to appear.

59. Normalized Matching Property of Restricted Subspace Lattices (with Huajun Zhang), SIAM J. Discrete Math., to appear.

60. An Erdos-Ko-Rado-Type Theorem in Coxeter Groups (with J. Zhang), European J. Combin., to appear.