The talk next week will be by James Sellers of the University of Minnesota, Duluth. We are back to our usual time, since the speaker is currently in Europe.
Talk Announcement:
Title: Partitions into Odd Parts with Designated Summands
Title: Partitions into Odd Parts with Designated Summands
Speaker: James Sellers (University of Minnesota, Duluth, USA)
When: Feb 20, 2025, 4:30 PM- 5:30 PM IST (12 Noon CET) (Note the time).
When: Feb 20, 2025, 4:30 PM- 5:30 PM IST (12 Noon CET) (Note the time).
Abstract
In 2002, Andrews, Lewis, and Lovejoy introduced the combinatorial objects which they called partitions with designated summands. These are built by taking unrestricted integer partitions and designating exactly one of each occurrence of a part. In that same work, Andrews, Lewis, and Lovejoy also studied such partitions wherein all parts must be odd, and they denoted the number of such partitions of size n by the function PDO(n).
In this talk, I will report on recent proofs of infinite families of divisibility properties satisfied by PDO(n). Some of these proofs follow in elementary fashion while others rely on modular forms (in work completed jointly with Shane Chern).
I will then transition to very recent joint work with Shishuo Fu in which we consider a "refined" view of PDO(n) based on ideas which originated with P. A. MacMahon. This new approach allows for a more combinatorial view of the well-known identity that, for all n,
In this talk, I will report on recent proofs of infinite families of divisibility properties satisfied by PDO(n). Some of these proofs follow in elementary fashion while others rely on modular forms (in work completed jointly with Shane Chern).
I will then transition to very recent joint work with Shishuo Fu in which we consider a "refined" view of PDO(n) based on ideas which originated with P. A. MacMahon. This new approach allows for a more combinatorial view of the well-known identity that, for all n,
$$PDO(2n) = \sum_{0 \leq k \leq n} PDO(k) PDO(n-k),$$
a result which is (trivially) proven via generating functions but which has eluded combinatorial proof for many years.
No comments:
Post a Comment