AdvOL Student Seminars and Defences
Asma Paracha, December 12, 2017, 15:30-16:00, ITB 201
Speaker:   Asma Paracha

Title:  Lyndon factors and periodicities in strings
AdvOL Optimization Seminars
Alexander Rosa, December 12, 2017, 16:30-17:30, ITB 201
Speaker:   Alexander Rosa
Department of Mathematics & Statistics
McMaster University

Title:  Reaction graphs of combinatorial configurations
Fields Institute Industrial Optimization Seminar, November 14, 2017
Speakers:   Christopher Swartz (McMaster University)
Jesus Flores-Carrillo (Praxair)

On the first Tuesday of each month, the Industrial Optimization Seminar is held at the Fields Institute. See the seminar series website for further information.
Home arrow Seminars arrow Invited seminars arrow Frantisek Franek, October 22, 2013, 16:30-17:30, ITB 201
Friday, 24 November 2017
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Frantisek Franek, October 22, 2013, 16:30-17:30, ITB 201
Speaker:   Frantisek Franek
Department of Computing and Software
Faculty of Engineering
McMaster University

Title:  How many double squares can a string contain?

Counting the types of squares rather than their occurrences, we consider the problem of bounding the number of distinct squares in a string. Fraenkel and Simpson showed in 1998 that a string of length n contains at most 2n distinct squares. Ilie presented in 2007 an asymptotic upper bound of 2n - Θ(log n). We show that a string of length n contains at most 5n/3 distinct squares. This new upper bound is obtained by investigating the combinatorial structure of double squares and showing that a string of length n contains at most 2n/3 double squares. In addition, the established structural properties provide a novel proof of Fraenkel and Simpson's result.

A joint work with A. Deza and A. Thierry.

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