Research Experiences
My mathematical interest is in combinatorial proofs of statements and identities through the use of discrete objects (such as tilings, graphs and triangulations) as models. My work so far has involved orthogonal polynomials, discrete analogs of topological theorems and enumeration of lattice points in polytopes. Small-world networks, spanning trees and applications of graph theory have figured prominently in work with students.
Below is a list of publications (* indicates an undergraduate student author).
- I. Gessel and P. Jayawant, A triple lacunary generating function for Hermite polynomials , Electronic Journal of Combinatorics 12(1) (2005), R30.
- P. Jayawant, M. Kosa, and C. Shannon, Reconstructing Curves from Sample Data , DIMACS Educational Module Series Module 08-5 (2008).
- K. Glavin* and P. Jayawant, Minimum spanning trees , Involve 2(4) (2009), pp. 437–448.
- A. Benjamin, L. Ericksen, P. Jayawant, and M. Shattuck, Combinatorial trigonometry with Chebyshev polynomials , J. Statist. Plann. Inference (2010), doi:10.1016/j.jspi.2010.01.011.
- I. Gessel and P. Jayawant, Multilinear generating functions for Charlier polynomials , J. Statist. Plann. Inference (2010), doi:10.1016/j.jspi.2010.01.019.
- P. Jayawant and P. Wong, A combinatorial analog of a theorem of F. J. Dyson, Topology and its Applications (2010), doi:10.1016/j.topol.2010.02.020.