Associate Teaching Professor, Mathematics
Niraj Khare is an associate teaching professor of mathematics with expertise in combinatorics, in particular extremal graph, extremal hypergraph theory and enumerative combinatorics.
Ph.D., Discrete Mathematics, Ohio State University, Columbus, OH
B.Sc. Honors, Mathematics, Indian Institute of Technology, Kharagpur, India
Area Of Expertise
Combinatorics, in particular extremal graph, extremal hypergraph theory and enumerative combinatorics.
The broad field of Khare's research is combinatorics, in particular extremal set theory, graph theory, hypergraph theory and enumerative combinatorics. Application of graph theory and hypergraph theory in developing algorithms based on new research involving constructional proofs over existential ones also interests Khare, as well as application of combinatorics to business, biology and physics. His work can be partitioned into two areas: work on graphs and hypergraphs, and work on enumerative combinatorics.
Graphs, hyper-graphs, parking functions, matchings, degree, independent set, enumeration, moments.
Moments of matching statistics, The Journal of Combinatorics, 8, 1-27, 2017. (Lorentz, R., and Yan, C.). https://dx.doi.org/10.4310/JOC.2017.v8.n1.a1
Graphs with restricted valency and matching number, Discrete Mathematics, 309(2009), 4176-4180 (with Niranjan Balachandran) doi:10.1016/j.disc.2008.10.007
On the size of a 3-uniform linear hypergraph, Discrete Mathematics, 334 (2014), 26-37 (http://www.journals.elsevier.com/discrete-mathematics/)
Generalization of Erdos-Gallai edge bound, European journal of Combinatorics, 43 (2015) 124-130 (with N. Mehta and N. Puliyambalath) (http://www.journals.elsevier.com/european-journal-of-combinatorics/).
Bivariate Goncarov Polynomials and Integer Sequences, Science China Mathematics, 57 (2014), 1561-1578 (with Rudolf Lorentz and Catherine Yan) http://link.springer.com/article/10.1007%2Fs11425-014-4827-x
Moments of permutation statistics and Central limit theorems. To appear in Advances in Applied Mathematics (with Stoyan Dimitrov) https://doi.org/10.48550/arXiv.2109.09183