On a faithful representation of Sturmian morphisms

Štěpán Starosta
Faculty of Information Technology, CTU in Prague

Date(s) : 27/03/2023   iCal
15 h 00 min - 16 h 00 min

The set of morphisms mapping any Sturmian sequence to a Sturmian sequence forms together with composition the so-called monoid of Sturm. For this monoid, we define a faithful representation by -matrices with integer entries. We find three convex cones in and show that a matrix is a matrix representing a Sturmian morphism if the three cones are invariant under multiplication by or . This property offers a new tool to study Sturmian sequences. We provide alternative proofs of four known results on Sturmian sequences fixed by a primitive morphism and a new result concerning the square root of a Sturmian sequence.



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