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SUMMARY:Niels Langeveld (Montanuniversität Leoben)
DTSTART:20220927T120000Z
DTEND:20220927T130000Z
DTSTAMP:20260423T021242Z
UID:OWNS/93
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/93/">$N
 $-continued fractions and $S$-adic sequences</a>\nby Niels Langeveld (Mont
 anuniversität Leoben) as part of One World Numeration seminar\n\n\nAbstra
 ct\nGiven the $N$-continued fraction of a number $x$\, we construct $N$-co
 ntinued fraction sequences in the same spirit as Sturmian sequences can be
  constructed from regular continued fractions. These sequences are infinit
 e words over a two letter alphabet obtained as the limit of a directive se
 quence of certain substitutions (they are S-adic sequences). By viewing th
 em as a generalisation of Sturmian sequences it is natural to study balanc
 edness. We will see that the sequences we construct are not 1-balanced but
  C-balanced for $C=N^2$. Furthermore\, we construct a dual sequence which 
 is related to the natural extension of the $N$-continued fraction algorith
 m. This talk is joint work with Lucía Rossi and Jörg Thuswaldner.\n
LOCATION:https://researchseminars.org/talk/OWNS/93/
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