Combinatorical and Algebraic Structures Seminar

Date:	6.11.2018
Speaker:	Vasek Chvatal, Dep. of Computer Science and Software Engineering Concordia University, Montreal
Title:	Oldenburger, Kolakoski, Keane
Abstract:	Jack Edmonds suggested that, while talking about successes in research may be gratifying to the speaker's ego, talking about failures could be more constructive. Following this suggestion, I will report on my failure to answer a question of Michael Sylvester Keane: is the density of 1s (and therefore also the density of 2s) in the sequence 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2,\ldots equal to 1/2? Defining properties of this sequence are that its k-th term is the length of its k-th run (= block of like numbers) and that its first term is 1. In keeping with a time-honoured tradition (that which we call a Steiner triple system was constructed by Thomas Penyngton Kirkman and that which we call a Hamiltonian cycle was introduced by the same Reverend Kirkman), it is called the Kolakoski sequence, even though it was introduced by Rufus Oldenburger.

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