Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, July 11, 2006, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Stefanie Gerke

Sequences with changing dependencies

Consider words over an alphabet with n letters. Fisher (1989) calculated the number of distinct words of length l assuming certain pairs of letters commute. In this talk we are interested in a more general setting where the pairs of letters that commute at a certain position of a word depend on the initial segment of the word. In particular, we show that if for each word at each position any letter fails to commute with a bounded number of other letters then the number of distinct words of length l is bounded by C^{n+l} for some constant~C. We use this result to obtain a lower bound on the number of diagonal flips required in the worst case to transform one n-vertex labelled triangulated planar graph into some other one. This has previously been proved by Sleator, Tarjan and Thurston (1992) by different methods.

Joint work with Paul Balister and Béla Bollobás.

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