DMS Combinatorics Seminar

Speaker: Nicholas Gaubatz (Auburn  University)

Title: Minimal Sizes of Out-Neighborhoods in the \(F\)-Lattice

Abstract: The classical isoperimetry problem is to determine the shape with minimal perimeter among all shapes of fixed volume. Analogs of this problem have been studied in the setting of lattices and polyominoes. We will discuss a variation of this problem posed by Joe Briggs, where we compute the sizes of minimal out-neighborhoods in the \(F\)-lattice. We will present some results toward this end via examples, focusing on the minimum values attained and the minimizers.

This is joint work with Haile Gilroy and Sean Grate.