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James Sellers(Penn State)

Tuesday, January 29
4:00 PM
135 TMCB

Topic: Personal Perspectives on m-ary Partitions

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