##### Department of Mathematics,

University of California San Diego

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### Combinatorics

## Kevin O Bryant

## The Permutation that Orders Fractional Parts and Nearly PeriodicWords

##### Abstract:

The permutation $pi$ of $1,2,ldots,n$ that satisfies> $$0 < { pi(1) alpha } < { pi(2) alpha } < cdots < { pi(n)alpha} < 1$$ ($alpha$ is any irrational) has been studied from a combinatorialviewpoint (S—s, Boyd) and from an analytic viewpoint (Schoi§engeier). I will present some results on algebraic properties of this permutation, the most significant being a mysterious appearance in the study of nearly periodic binary words (a.k.a., Sturmian words) with the representation theory of symmetric groups.

Host:

### October 29, 2002

### 3:00 PM

### AP&M 7321

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