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SUMMARY:Jana Lepšová (Czech Technical University in Prague\, Université
  de Bordeaux)
DTSTART:20231114T130000Z
DTEND:20231114T140000Z
DTSTAMP:20260423T053135Z
UID:OWNS/121
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/121/">D
 umont-Thomas numeration systems for ℤ</a>\nby Jana Lepšová (Czech Tech
 nical University in Prague\, Université de Bordeaux) as part of One World
  Numeration seminar\n\n\nAbstract\nWe extend the well-known Dumont-Thomas 
 numeration system to ℤ by considering two-sided periodic points of a sub
 stitution\, thus allowing us to represent any integer in ℤ by a finite w
 ord (starting with 0 when nonnegative and with 1 when negative). We show t
 hat an automaton returns the letter at position $n \\in ℤ$ of the period
 ic point when fed with the representation of $n$. The numeration system na
 turally extends to $ℤ^d$. We give an equivalent characterization of the 
 numeration system in terms of a total order on a regular language. Lastly\
 , using particular periodic points\, we recover the well-known two's compl
 ement numeration system and the Fibonacci analogue of the two's complement
  numeration system.\n
LOCATION:https://researchseminars.org/talk/OWNS/121/
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