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.
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Research Interests
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Combinatorics: Enumerative combinatorics, partially ordered
sets, group arrangements, polytopes and polyhedra.
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Graph Theory: Graph polynomials, Graph learning, graph
convolutional network, graph database, knowledge graphs.
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Topology/Geometry: Subspace arrangements, cellular spaces, semi-algebraic
sets, toric variety, weight homology.
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Courses
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Math3343
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Math113
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Math111
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Math2343
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Math2721
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Math4221
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Math4821B
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Math5380
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Poems
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Mathlink
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Preprints
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Subspace Arrangements and q-Analog
of Poincar?/span>
Series, preprint.
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Gauss-Bonnet formula, finiteness condition, and
asymptotic characterization for graphs embedded in surfaces
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preprint.
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Publications
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2006--2010:
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The flow and
tension spaces and lattices of signed graphs.
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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.
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Gauss-Bonnet formula, finiteness condition, and
asymptotic characterization for graphs embedded in surfaces. (with Guantao Chen) , Graphs Combin. 24 (2008), 159--183.
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2001--2005:
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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.
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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.
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A simplified
elementary proof of Hadwiger's volume theorem, Geometriae Dedicata,
105(2004), 107-120.
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The Pick theorem and the proof of the reciprocity law
for Dedekind sums, Annals Combin.,
7(2003), 425-439.
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On
semi-Eulerian partially ordered sets with boundary (with Lau,
M.), European J. Combin., 24(2003),
955-968.
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Lattice points, Dedekind sums, and
Ehrhart polynomials of lattice polyhedra, Discrete
& Computational Geometry, 28(2002), 175-199.
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Generalizations
of Knopp's identity (with Sun,
Z.W.), J. Number Theory, 97(2002), 186-198.
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Graph homotopy
and Graham homotopy (with Yau, S.-T. and Yeh, Y.-N.), Discrete
Mathematics, 241(2001), 153-170.
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1996---2000:
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Counting lattice points of
rational polyhedra (with Turaev, V.), Advances in Mathematics, 155(2000),
84-97.
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On
characteristic polynomials of subspace arrangements, Journal
of Combinatorial Theory Series A, 90(2000), 347-352.
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Minkowski Algebra I: A
convolution theory of closed convex sets and relatively open convex sets, Asian
Journal of Mathematics, 3(1999), 609-634.
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A note on
cyclic colorations and minimal triangulations (with Lawrencenko, S.), Yokohama math. J., 47(1999),
93-99.
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Eulerian
2-strata spaces (with Yan, M.), Journal of Combinatorial Theory Series A,
85(1999), 1-28.
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Domination
Number and Neighborhood Conditions (with Zhou, S.M.), Discrete Mathematics,
195(1999), 81-91.
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Eulerian
Stratification of Polyhedra (with Yan,
M.), Advances in Applied Mathematics, 21(1998), 22-57.
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Singularity
from Eulerian viewpoint (with Yan, M.), Proceedings of Steklov Mathematical Institute, 221(1998), 296-311.
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Structural
Characterization of Projective Flexibility (with Lawrencenko, S.), Discrete Mathematics,
188(1998), 233-238.
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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.
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The Geometric
Cone Relations for Simplicial and Cubical Complexes (with Yan,
M.), Discrete Mathematics, 183(1998), 39-46.
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The Upper
Bounds for f-Domination Numbers of Graphs (with Zhou,
S.M.), Discrete Mathematics, 185(1998), 239-243.
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Linear
Conditions on the Number of Faces of Manifolds with Boundary (with Yan,
M.), Advances in Applied Mathematics, 19(1997), 144-168.
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Pansystems Optimization,
Generalized Principles of Optimality, and Fundamental Equations of Dynamic
Programming, Kybernetes, 26(1997),
316-333.
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Parametric Möbius Inversion Formulas, Discrete
Mathematics, 169(1997), 211-215.
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Geometric Dehn-Sommerville Relations, Journal
of Combinatorial Theory, Series A, 73(1996), 142-151.
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The Incidence
Algebra of Polyhedra over the Minkowski
Algebra, Advances in Mathematics, 118(1996), 337-365.
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1991---1995:
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The Mixed
Volumes and Geissinger Multiplications of Convex
Sets, Studies in Applied Mathematics, 91(1994), 39-50.
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Totally
Invariant Set Functions of Polynomial Type (with Rota,
G.-C.;), Communications on Pure and Applied
Mathematics, 47(1994), 187-197.
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Some
Explanations of Dobinski's Formula (with Yeh, Y.N.), Studies in Applied Mathematics,
92(1994), 191-199.
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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.
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On the Euler
Characteristics of Finite Unions of Convex Sets, Discrete
and Computational Geometry, 10(1993), 79-93.
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The Gram-Sommerville and Gauss-Bonnet Theorems and Combinatorial
Geometric Measures for Noncompact Polyhedra, Advances in Mathematics, 91(1992),
269-291.
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1983---1990:
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Some Pansystem Models of General Equilibrium in Economics (with Wu,
X.M.), Kybernetes, 14(1985), 37-43.
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Pansystems Clustering
Method and Its Application to Classification of Fuzzy things, Fuzzy
Mathematics, 3(1984), 51-58.
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Pansystems Investigation
of ε-equilibrium under Fuzzy Preferences, Fuzzy
Mathematics, 4(1984), 93-98.
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Quasi-transitivity
and Problem of Social Choice (with Wu, S.Z.), Science Exploration,
4(1984), 47-52.
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On the Problem
of Equilibrium under Quasi-transitive Preferences (with Wu, S.
Z.), Exploration of Nature, 1(1984), 29-36.
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Pansystems
Investigations of Quotient Systems and Its Application, Science
Exploration, 4(1983), 81-88.
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Some Logic
Transforming Conservation of Semi-equivalence Pansystems
Theory, Science Exploration, 3(1983), 87-94.
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