Fu Liu 刘拂 | |
| Ostensible contact info: 3220 Mathematical Science Building (530) 754-9381 Actual contact info: |
Mailing address: Department of Mathematics University of California, Davis One Shields Avenue Davis, CA 95616 USA |
| Research interests: Enumerative and algebraic combinatorics. | |
Here is my curriculum vitae (or PDF).
Teaching info: In Spring 2008, I am teaching MAT16B and also offering a reading course on posets.
Ehrhart
polynomials of cyclic polytopes (arXiv) Fall 2004
A paper proving the conjecture made in math.CO/0402148 about the
coefficients of the
Ehrhart polynomials of cyclic polytopes.
Journal of Combinatorial Theory
Ser. A 111 (2005), no. 1, 111-127.
(k,m)-Catalan numbers and Hook length polynomials
for plane trees, with Rosena Du (arXiv) Winter 2005
A short paper defining the hook length polynomials for m-ary trees and
plane forests, and introducing a new generalization of Catalan numbers, by
using which we prove our hook length polynomials have a simple binomial
expression.
European Journal of Combinatorics 28 (2007), no. 4, 1312-1321.
Hook length polynomials for plane forests of a
certain type (arXiv) Summer 2005
A short note defining the hook length polynomials for plane forests of a
given degree sequence type. Some other enumerative results on trees are also
given.
To appear in Annals of Combinatorics.
Ehrhart polynomials of lattice-face
polytopes (arXiv) Fall 2005
A paper defining a new family of polytopes, lattice-face polytopes, which
is a generalization of cyclic polytopes. We show that the Ehrhart polynomial
of a lattice-polytope has the same simple form as cyclic polytopes.
Transactions of the AMS 360 (2008), no. 6, 3041-3069.
The irreducibility of
certain pure-cycle Hurwitz spaces, with Brian Osserman (arXiv) Fall
2006
We use a combination of geometric and group-theoretic techniques to prove
that Hurwitz spaces of genus-0 covers of the projective line having a single
ramified point over each branch point are irreducible.
To appear in the American Journal of Mathematics.
Formulas for the volumes of the polytope of doubly-stochastic matrices and its faces, with Jesus A. De Loera and Ruriko Yoshida (arXiv) Fall 2006 - Winter 2007
We provide an explicit combinatorial formula for the volume of the polytope of n by n doubly-stochastic matrices, also known as the Birkhoff polytope. We do this through finding the multivariate generating function for the lattice points of the polytope.
Submitted for publication.