Speaker: Dr. Rajat Gupta Affilitation: University of Texas at Tyler Title: Smallest parts function of Andrews, sum-of-tails identities: A combinatorial excursion Abstract: See attached PDF file Venue: Ramanujan Hall Time: 14:30-15:30 hrs Date: 26th July 2024.
Title: Smallest parts function of Andrews, sum-of-tails identities: A combinatorial excursion
Abstract: In the first half of the talk, we first review a classical combinatorial result of Ramanujan and Uchimura, which states that the difference between the sum of the smallest parts of the partitions of n into an odd number of distinct parts and the corresponding sum for an even number of distinct parts is equal to the number of divisors of n. We will see its connection with a problem arising from the theory of random acyclic graphs. The second half will be devoted to some-of-tails identities and extensions of the above theorem with its application. The works presented here are the joint work with Rahul Kumar, Noah Lebowitz-Lockard and Professor Joseph Vandehey.