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 Events
Bob Hough
Institute for Advanced Study, Princeton
Fri 12 Feb 2016, 3:00pm
Department Colloquium
MATX 1100
Covering systems of congruences and the Lovasz Local Lemma
MATX 1100
Fri 12 Feb 2016, 3:00pm-4:00pm

Abstract

The Lov\'{a}sz Local Lemma is a powerful technique from probabilistic combinatorics for treating many rare events with localized dependence structure.  I discuss the local lemma and its application in my negative solution to the following problem of Erd\H{o}s.

A distinct covering system of congruences is a collection of arithmetic progressions
 
a_i \bmod m_i, \qquad 1 < m_1 < m_2 < ... < m_k

whose union is the integers. Can m_1 be arbitrarily large?

Note for Attendees

Refreshments will be served in MATH 125 before the colloquium.
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