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SUMMARY:q-analogs of rational numbers: from Ostrowski numeration systems t
 o perfect matchings
DTSTART:20260903T123000Z
DTEND:20260903T133000Z
DTSTAMP:20260910T060800Z
UID:indico-event-17088@indico.math.cnrs.fr
CONTACT:kellendonk@math.univ-lyon1.fr\;athomas@math.univ-lyon1.fr
DESCRIPTION:Speakers: Sébastien Labbé (Bordeaux)\n\nWe consider the q-de
 formation of rational numbers introduced recently by Morier-Genoud and Ovs
 ienko. We propose three enumerative interpretations of these q-rationals: 
 in terms of a new version of Ostrowski's numeration system for integers\, 
 in terms of order ideals of fence posets and in terms of perfect matchings
  of snake graphs. Contrary to previous results which are restricted to rat
 ional numbers greater than one\, our interpretations work for all positive
  rational numbers and are based on a single combinatorial object for defin
 ing both the numerator and denominator. The proofs rest on order-preservin
 g bijections between posets over these objects. We recover a formula for a
  q-analog of Markoff numbers. We also deduce a fourth interpretation given
  in terms of the integer points inside a polytope in R^k on both sides of 
 a hyperplanewhere k is the length of the continued fraction expansion. Thi
 s is joint work with Jean-Christophe Aval available at arXiv:2511.11290.\n
 \nhttps://indico.math.cnrs.fr/event/17088/
LOCATION:Salle Fokko du Cloux (Bat. Braconnier)
URL:https://indico.math.cnrs.fr/event/17088/
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