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Combinatorics Seminar - Christopher Donnay

Donnay
October 3, 2024
1:50 pm - 2:45 pm
Enarson Classroom Building EC0322

Christopher Donnay
The Ohio State University

Title
The asymptotics of redistricting the n\times n grid

Abstract
Redistricting is the act of dividing a region into districts for electoral representation. Motivated by this application, we study two questions: How many ways are there to partition the n\times n grid into n contiguous districts of equal size? How many of these partitions are "compact"? We give asymptotic bounds on the number of plans: a lower bound of roughly 1.41^{n^2} and an upper bound of roughly 3.21^{n^2}. We then use the lower bound to show that most plans are not compact. This is joint work with Matthew Kahle.

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Seminar - Combinatorics