### On the number of factors in codings of three interval exchange

*Petr Ambrož, Anna Frid, Zuzana Masáková, Edita Pelantová*

#### Abstract

We consider exchange of three intervals with permutation
(3,2,1). The aim of this paper is to count the
cardinality of the set 3iet(N) of all words of length
N which appear as factors in infinite words coding such
transformations. We use the strong relation of 3iet words and words
coding exchange of two intervals, i.e., Sturmian words. The known
asymptotic formula
#2iet(N)/N

^{3}∼1/π^{2}for the number of Sturmian factors allows us to find bounds 1/3π^{2}+ o(1) ≤# 3iet(N)/N^{4}≤ 2/π^{2}+ o(1).Full Text: PDF PostScript