Beifang Chen

Professor

Department of Mathematics
Hong Kong University of Science and Technology
Clear Water Bay, Kowloon
Hong Kong

Tel: (852) 2358-7449 Fax: (852) 2358-1643
Email: mabfchen@ust.hk      

Dr. Chen is Professor of Mathematics in HKUST and guest Professor in Nankai University. He was an applied mathematics instructor in Massachusetts Institute of Technology before he joined HKUST in Fall 1993.

Research Interests

   
  Combinatorics
  Graph Theory
  Topology/Geometry
 

Courses

   
  Math3343 ----- Combinatorial Analysis
  Math113 ----- Introduction to Linear Algebra
  Math111 ----- Linear Algebra
  Math2343 ----- Discrete Structure
  Math2721 ----- Concepts of Mathematics
  Math4221 ----- Euclidean and Non-Euclidean Geometry
  Math300L ----- Introduction to Graph Theory
 
Poems
   
  Counting   To Shing-Tung Yau
  To Gian-Carlo Rota   To Shiing-Shen Chern
  Vectors in space   The Victoria harbour
  Gathering   Swing a little boat
  To Fuji Zhang   To Chen-Ning Yang
  HKUST(1)   HKUST(2)
  On the train home   Boat and boy
 
Mathlink
   
  AMS   Combinatorics Net
 
Preprints

 

Subspace Arrangements and q-Analog of Poincar?/span> Series, preprint.
Gauss-Bonnet formula, finiteness condition, and asymptotic characterization for graphs embedded in surfaces , preprint.
   
Publications
 
 2006--2010:
   
The flow and tension spaces and lattices of signed graphs.
A bijection for Eulerian-equivalence classes of totally cyclic orientations. (with Arthur L.B. Yang and Terence Y.J. Zhang) , Graphs Combin. 24 (2008), 519--530.
Gauss-Bonnet formula, finiteness condition, and asymptotic characterization for graphs embedded in surfaces. (with Guantao Chen) , Graphs Combin. 24 (2008), 159--183.
 2001--2005:
   
Problems from the Cottonwood Room (with Beck, M; Fukshansky, L.; Haase, C.; Knutson, A.; Reznick, B.; Robins, S. and Schürmann, A.), in: Integer Points in Polyhedra -- Geometry, Number Theory, Algebra, Optimization, 179-191, Contemp. Math., 374, Amer. Math. Soc., Providence, RI, 2005.
   
Ehrhart polynomials of lattice polyhedral functions, in: Integer Points in Polyhedra -- Geometry, Number Theory, Algebra, Optimization, 37-63, Contemp. Math., 374, Amer. Math. Soc., Providence, RI, 2005.
   
A simplified elementary proof of Hadwiger's volume theorem, Geometriae Dedicata, 105(2004), 107-120.
   
  The Pick theorem and the proof of the reciprocity law for Dedekind sums, Annals Combin., 7(2003), 425-439.
   
On semi-Eulerian partially ordered sets with boundary (with Lau, M.), European J. Combin., 24(2003), 955-968.
   
Lattice points, Dedekind sums, and Ehrhart polynomials of lattice polyhedra, Discrete & Computational Geometry, 28(2002), 175-199.
   
Generalizations of Knopp's identity (with Sun, Z.W.), J. Number Theory, 97(2002), 186-198.
   
Graph homotopy and Graham homotopy (with Yau, S.-T. and Yeh, Y.-N.), Discrete Mathematics, 241(2001), 153-170.
   
 1996---2000:        
   
Counting lattice points of rational polyhedra (with Turaev, V.), Advances in Mathematics, 155(2000), 84-97.
   
On characteristic polynomials of subspace arrangements, Journal of Combinatorial Theory Series A, 90(2000), 347-352.
   
Minkowski Algebra I: A convolution theory of closed convex sets and relatively open convex sets, Asian Journal of Mathematics, 3(1999), 609-634.
   
A note on cyclic colorations and minimal triangulations (with Lawrencenko, S.), Yokohama math. J., 47(1999), 93-99.
   
Eulerian 2-strata spaces (with Yan, M.), Journal of Combinatorial Theory Series A, 85(1999), 1-28.
   
Domination Number and Neighborhood Conditions (with Zhou, S.M.), Discrete Mathematics, 195(1999), 81-91.
   
Eulerian Stratification of Polyhedra (with Yan, M.), Advances in Applied Mathematics, 21(1998), 22-57.
   
Singularity from Eulerian viewpoint (with Yan, M.), Proceedings of Steklov Mathematical Institute, 221(1998), 296-311.
   
Structural Characterization of Projective Flexibility (with Lawrencenko, S.), Discrete Mathematics, 188(1998), 233-238.
   
Weight Functions, Double Reciprocity Laws, and Volume Formulas for Lattice Polyhedra, Proceedings of the National Academy of Sciences of the United States of America, 95(1998), 9093-9098.
   
The Geometric Cone Relations for Simplicial and Cubical Complexes (with Yan, M.), Discrete Mathematics, 183(1998), 39-46.
   
The Upper Bounds for f-Domination Numbers of Graphs (with Zhou, S.M.), Discrete Mathematics, 185(1998), 239-243.
   
Linear Conditions on the Number of Faces of Manifolds with Boundary (with Yan, M.), Advances in Applied Mathematics, 19(1997), 144-168.
   
Pansystems Optimization, Generalized Principles of Optimality, and Fundamental Equations of Dynamic Programming, Kybernetes, 26(1997), 316-333.
   
Parametric Möbius Inversion Formulas, Discrete Mathematics, 169(1997), 211-215.
   
Geometric Dehn-Sommerville Relations, Journal of Combinatorial Theory, Series A, 73(1996), 142-151.
   
The Incidence Algebra of Polyhedra over the Minkowski Algebra, Advances in Mathematics, 118(1996), 337-365.
   
 1991---1995:        
   
The Mixed Volumes and Geissinger Multiplications of Convex Sets, Studies in Applied Mathematics, 91(1994), 39-50.
   
Totally Invariant Set Functions of Polynomial Type (with Rota, G.-C.;), Communications on Pure and Applied Mathematics, 47(1994), 187-197.
   
Some Explanations of Dobinski's Formula (with Yeh, Y.N.), Studies in Applied Mathematics, 92(1994), 191-199.
   
The Induced Linear Maps on Minkowski Algebras of Convex Sets, Proceedings of the First International Tainan-Moscow Workshop (1994), (Fong, Y., Knauer, U. & Mikhalev, A.V., eds.), pp. 181-198., Water de Gruyter & Co., Berlin, 1996.
   
On the Euler Characteristics of Finite Unions of Convex Sets, Discrete and Computational Geometry, 10(1993), 79-93.
   
The Gram-Sommerville and Gauss-Bonnet Theorems and Combinatorial Geometric Measures for Noncompact Polyhedra, Advances in Mathematics, 91(1992), 269-291.
   
 1983---1990:        
   
Some Pansystem Models of General Equilibrium in Economics (with Wu, X.M.), Kybernetes, 14(1985), 37-43.
   
Pansystems Clustering Method and Its Application to Classification of Fuzzy things, Fuzzy Mathematics, 3(1984), 51-58.
   
Pansystems Investigation of ε-equilibrium under Fuzzy Preferences, Fuzzy Mathematics, 4(1984), 93-98.
   
Quasi-transitivity and Problem of Social Choice (with Wu, S.Z.), Science Exploration, 4(1984), 47-52.
   
On the Problem of Equilibrium under Quasi-transitive Preferences (with Wu, S. Z.), Exploration of Nature, 1(1984), 29-36.
   
Pansystems Investigations of Quotient Systems and Its Application, Science Exploration, 4(1983), 81-88.
   
Some Logic Transforming Conservation of Semi-equivalence Pansystems Theory, Science Exploration, 3(1983), 87-94.