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...

This paper investigates a combinatorial approach to vector field topology. The theoretical basis is given by Robin Forman’s work on a combinatorial Morse theory for dynamical systems defined on general simplicial complexes. We formulate Forman’s theory in a graph theoretic setting and provide a simple algorithm for the construction and topological simplification of combinatorial vector fields o...

Faculty of Arts Mathematics Department Master of Literature by Padraig Ó Catháin Hadamard matrices are an important item of study in combinatorial design theory. In this thesis, we explore the theory of cocyclic development of Hadamard matrices in terms of regular group actions on the expanded design. To this end a general theory of both group development and cocyclic development is formulated....

This review gives a history of the construction of quantum field theory on four-dimensional spacetime using combinatorial techniques, and recent developments of the theory towards a combinatorial construction of quantum gravity.

Submodular functions and related polyhedra play an increasing role in combinatorial optimization. The present survey-type paper is intended to provide a brief account of this theory along with several applications in graph theory and combinatorial optimization.

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...

the set covering problem (scp) is a well-known combinatorial optimization problem. this paper investigates development of a local branching approach for the scp. this solution strategy is exact in nature, though it is designed to improve the heuristic behavior of the mixed integer programming solver. the algorithm parameters are tuned by design of experiments approach. the proposed method is te...