BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Narad Rampersad (University of Winnipeg) DTSTART:20200505T123000Z DTEND:20200505T133000Z DTSTAMP:20260423T052924Z UID:OWNS/1 DESCRIPTION:Title: Ost rowski numeration and repetitions in words\nby Narad Rampersad (Univer sity of Winnipeg) as part of One World Numeration seminar\n\n\nAbstract\nO ne of the classical results in combinatorics on words is Dejean's Theorem\ , which specifies the smallest exponent of repetitions that are avoidable on a given alphabet. One can ask if it is possible to determine this quan tity (called the *repetition threshold*) for certain families of infinite words. For example\, it is known that the repetition threshold for Sturmi an words is 2+phi\, and this value is reached by the Fibonacci word. Rece ntly\, this problem has been studied for *balanced words* (which generaliz e Sturmian words) and *rich words*. The infinite words constructed to res olve this problem can be defined in terms of the Ostrowski-numeration syst em for certain continued-fraction expansions. They can be viewed as *Ostr owski-automatic* sequences\, where we generalize the notion of *k-automati c sequence* from the base-k numeration system to the Ostrowski numeration system.\n LOCATION:https://researchseminars.org/talk/OWNS/1/ END:VEVENT END:VCALENDAR