Combinatorics seminar

Monday, 22 January 2024, 14:30-15:30 hrs

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Venue: Ramanujan Hall

Host: S. Krishnan

Speaker: Hiranya Dey

Affiliation: Indian Institute of Science, Bengaluru

Title: On the sum of the entries in the character table of a finite group

Abstract: In 1961, Solomon proved that the sum of all the entries (total sum) in the character table of a finite group does not exceed the cardinality of the group. In this
talk, we will see that for symmetric groups, the total sum is asymptotically the same as
the first column sum. We will also prove that similar results hold for hyperoctahedral
groups and demihyperoctahedral groups. We will also see the generating function for total
sum for generalized symmetric groups which uses Flajolet's work on continued fractions.
This is a joint work with Arvind Ayyer and Digjoy Paul.