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SUMMARY:Jacques Sakarovitch (Irif\, CNRS\, and Télécom Paris)
DTSTART:20201117T133000Z
DTEND:20201117T143000Z
DTSTAMP:20260423T040004Z
UID:OWNS/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/24/">Th
 e carry propagation of the successor function</a>\nby Jacques Sakarovitch 
 (Irif\, CNRS\, and Télécom Paris) as part of One World Numeration semina
 r\n\n\nAbstract\nGiven any numeration system\, the carry propagation at an
  integer $N$ is the number of digits that change between the representatio
 n of $N$ and $N+1$. The carry propagation of the numeration system as a wh
 ole is the average carry propagations at the first $N$ integers\, as $N$ t
 ends to infinity\, if this limit exists. \n\nIn the case of the usual base
  $p$ numeration system\, it can be shown that the limit indeed exists and 
 is equal to $p/(p-1)$. We recover a similar value for those numeration sys
 tems we consider and for which the limit exists. \n\nThe problem is less t
 he computation of the carry propagation than the proof of its existence. W
 e address it for various kinds of numeration systems: abstract numeration 
 systems\, rational base numeration systems\, greedy numeration systems and
  beta-numeration. This problem is tackled with three different types of te
 chniques: combinatorial\, algebraic\, and ergodic\, each of them being rel
 evant for different kinds of numeration systems. \n\nThis work has been pu
 blished in Advances in Applied Mathematics 120 (2020). In this talk\, we s
 hall focus on the algebraic and ergodic methods. \n\nJoint work with V. Be
 rthé (Irif)\, Ch. Frougny (Irif)\, and M. Rigo (Univ. Liège).\n
LOCATION:https://researchseminars.org/talk/OWNS/24/
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