### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Brian Nakamura**, Rutgers University, bnaka {at} math [dot] rutgers [dot] edu
** Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Integer Subsets with High Volume and Low Perimeter

Speaker: **Patrick Devlin**, Rutgers University

Date: Thursday, November 1, 2012 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

We explore a certain variation of the isoperimetric problem in which integer subsets take the role of geometric figures. In particular, after defining some simple notions of "perimeter" and "volume" for integer subsets, we ask the question "Among all subsets with volume n, what is the smallest possible perimeter?" For n=1, 2, 3, ..., this gives rise to an integer sequence, which will be the primary focus of the talk. We will also discuss the structure of these optimal subsets.

The talk will involve combinatorics, recurrence relations, algorithms, intricate fractal-type symmetries, a wee bit of analysis, and (of course) experimental math will ultimately come to the rescue. No background knowledge whatsoever is required (or assumed). The driving questions explored in the talk were first posed in a paper by Miller, Morgan, Newkirk, Pedersen and Seferis in 2011, and the talk itself will be based on a 2012 article in Integers by the same name.

See: http://www.math.rutgers.edu/~bnaka/expmath/