My research interests lie in Discrete Mathematics, especially Combinatorics, Graph Theory, Combinatorial Geometry, and Combinatorial Number Theory. For me, the most exciting aspect of working in discrete mathematics is the prevalence of combinatorial problems in various fields of mathematics and various applications to Computer Science and real life problems such as building transmitters in a t...

In this lecture I will discuss the application of some well known and less well known theorems in combinatorial analysis to various other branches of mathematics. In other words I will not mention combinatorial types of reasoning the use of which is of course very wide-spread (e.g. the classical proof of Carleson on the almost everywhere convergence of Fourier series of functions in L2 is full ...

The paper Proofs Without Syntax [Annals of Mathematics, to appear] introduced the notion of a combinatorial proof for classical propositional logic. The present paper uses combinatorial proofs to define a semantics for classical propositional sequent calculus, an inductive translation from sequent proofs to combinatorial proofs. The semantics is abstract and efficient: abstract in the sense tha...

s for talks to be presented in the CCCS 98 Workshop Instructional Lectures Cryptography and Combinatorial Designs Charles J. Colbourn, Dorothean Professor of Computer Science University of Vermont In this series of five lectures, we explore some of the many problems in cryptography where combinatorial designs have played a substantial role. To set the stage, we review some ideas from classical ...

This paper is an introduction to combinatorial knot theory via state summation models for the Jones polynomial and its generalizations. It also a story about developments that ensued in relation discovery of remembrance Vaughan his mathematics.

R.C. Jain Department of Computer Applications, Samrat Ashok Technological Institute, Vidisha, M.P. E-mail: [email protected] -------------------------------------------------------------------ABSTRACT----------------------------------------------------------------Association rule mining and classification are two important techniques of data mining in knowledge discovery process. Integration...

Combinatorial objects such as rooted trees that carry a recursive structure have found important applications recently in both mathematics and physics. We put such structures in an algebraic framework of operated semigroups. This framework provides the concept of operated semigroups with intuitive and convenient combinatorial descriptions, and at the same time endows the familiar combinatorial ...

Chung, F., P. Diaconis and R. Graham, Universal cycles for combinatorial structures, Discrete Mathematics 110 (1992) 43-59 In this paper, we explore generalizations of de Bruijn cycles for a variety of families of combinatorial structures, including permutations, partitions and subsets of a finite set.