Evaluation of determinants with residues, Hankel determinants of combinatorial numbers, and their connections to algebraic curves and hypergeometric functions.
Implementing Organization
Principal Investigator
Dr. Gautam Kalita
Indian Institute Of Information Technology, Guwahati, Assam
Project Overview
The main subject matter of the proposed project is determinants involving residues, sequences of combinatorial numbers, and related objects. We propose to evaluate and express determinants of matrices involving residues in terms of character sums, elliptic curves, and hypergeometric functions. We are also interested to investigate Hankel determinant of sequences of numbers and polynomials that appeared in combinatorics, the theory of graphs, and coding theory. All these evaluations shall be based on combinatorial technique, linear algebra, operator theory, properties of orthogonal polynomials, continued fraction, properties of characters, and theory of finite fields.
Indian Institute Of Information Technology, Guwahati, Assam
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