PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Robert Vaughan, Mihran Papikian, Ae Ja Yee, Kirsten Eisentraeger.

Title:Connections Between Path Partitions and Restricted m-ary Partitions
Seminar:Algebra and Number Theory Seminar
Speaker:James Sellers, Penn State University
Abstract:
In this talk, we will describe unique path partitions (whose motivation comes from representation theory of the symmetric group). Once this introduction is complete, we will discuss an explicit characterization of the unique path partitions of n (or up-partitions for short) in terms of partitions we call strongly decreasing (and which are closely related to the non-squashing partitions of Sloane and JAS). We then discuss numerous connections between up-partitions and certain types of binary partitions. Thanks to such connections with binary partitions, we conjecture and prove various arithmetic properties of u(n), the number of unique path partitions of n. We will close the talk with a discussion of generalizations to certain types of m-ary partitions as well as very recent work on arithmetic properties satisfied by such m-ary partition functions. This talk will touch on joint works of Christine Bessenrodt, Jorn Olsson, and JAS; George Andrews, Aviezri Fraenkel, and JAS; and George Andrews, Eduardo Brietzke, Oystein Rodseth, and JAS.

Room Reservation Information

Room Number:MB106
Date:02 / 11 / 2016
Time:11:15am - 12:05pm