October 3, 2024
1:50 pm
-
2:45 pm
Enarson Classroom Building EC0322
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2024-10-03 13:50:00
2024-10-03 14:45:00
Combinatorics Seminar - Christopher Donnay
Christopher DonnayThe Ohio State UniversityTitleThe asymptotics of redistricting the n\times n gridAbstractRedistricting 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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2024-10-03 13:50:00
2024-10-03 14:45:00
Combinatorics Seminar - Christopher Donnay
Christopher DonnayThe Ohio State UniversityTitleThe asymptotics of redistricting the n\times n gridAbstractRedistricting 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.
Enarson Classroom Building EC0322
America/New_York
public
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.
