SEMINAR: Congruences and the multiplicities of parts

Guest: Mohammed Lamine Nadji, The University of Science and Technology Houari Boumediene

Title: Congruences and the multiplicities of parts

Date/Time: October 9, 2024, 13:40

Location: FENS  L062

Abstract: We introduce several combinatorial properties of three classes of integer partitions:

1. s-modular partitions: A class consisting of partitions into parts with a number of occurrences (i.e., multiplicity) congruent to 0 or 1 modulo s.

2. s-congruent partitions: These generalize Sellers' partitions into parts not congruent to 2 modulo 4.

3. s-duplicate partitions: This class includes partitions having distinct odd parts, which are enumerated by the function mypod(n) as a special case.

We also present a generalization for Alladi's series expansion for the product generating function of mypod(n) and show that Andrews' generalization of Göllnitz-Gordon identities coincides with the number of partitions into parts that are simultaneously s-congruent and t-distinct (where parts appear fewer than t times).