James Sellers(Penn State)

Event Details

  • Date: Tuesday, Jan 29th 2019 4:00pm
  • Venue: 135 TMCB
  • Categories:
  • Topic: Personal Perspectives on m-ary Partitions
  • Speaker: James Sellers
  • College/Organization: Penn State University

A great deal of my research journey has involved the study of m-ary partitions.
These are integer partitions wherein each part must be a power of a fixed
integer m > 1. Beginning in the late 1960s, numerous mathematicians
(including Churchhouse, Andrews, Gupta, and Rodseth) studied divisibility
properties of m-ary partitions. In this talk, I will discuss work I completed
with Rodseth which generalizes the results of Andrews and Gupta from the
1970s. I will then discuss several problems related to m-ary partitions,
including my work with Neil Sloane on non-squashing stacks of boxes, an
application of m-ary partitions to objects known as “unique path partitions”
(which are motivated from representation theory of the symmetric group),
as well as very recent work with George Andrews and Aviezri Fraenkel on the
characterization of the number of m-ary partitions of n modulo m. Throughout
the talk, I will attempt to highlight various aspects of the research related
to symbolic computation.
Refreshments at 3:30 294 TMCB