Indistinguishable asymptotic pairs

Sebastián Barbieri
Universidad de Santiago de Chile

Date(s) : 21/11/2022   iCal
15 h 00 min - 16 h 00 min

We say two bi-infinite words are asymptotic if they differ in finitely many coordinates. We say they are indistinguishable if for any finite word w, the number of occurrences of w that intersect the set of differences in each of them is the same. In this talk we will study these objects and show that they are very closely related to Sturmian configurations. We will also show that a higher-dimensional analogue of the theorem holds, and as an application of this result we will provide a formula for computing the complexity of a multidimensional Sturmian configuration on any finite connected support. This is joint work with S. Labbé.

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