Rupam.Barman

Affiliation: Indian Institute of Technology Guwahati

Title Of Talk: Hook length inequalities for t-regular partitions

Abstract: Integer partitions are fundamental objects in combinatorics, geometry, mathematical physics, number theory, and representation theory. In particular, hook lengths of partitions arise in the study of class numbers of imaginary quadratic fields. Other than the ordinary partition function, hook lengths have also been studied for several restricted partition functions, for example, partitions into odd parts, partitions into distinct parts, and self conjugate partitions. Recently, Ballantine et al. and Craig et al. studied hook length inequalities in partitions into odd parts and partitions into distinct parts. Motivated by the works of Ballantine et al. and Craig et al., we have studied hook length inequalities for t-regular partitions. In this talk, we present several hook length inequalities for t-regular partitions. This is a joint work with Dr. Gurinder Singh.

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