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SUMMARY:Asymptotic bijection and scaling limits for factorizations of a lo
 ng cycle
DTSTART:20260409T120000Z
DTEND:20260409T130000Z
DTSTAMP:20260408T142900Z
UID:indico-event-15781@indico.math.cnrs.fr
DESCRIPTION:Speakers: Paul Thévenin (Angers)\n\nConsider factorizations o
 f the long cycle $(1\,2 \\ldots\,n)$ into a product of transpositions\, in
  the symmetric group $S_n$. It is known that one needs at least $n-1$ tran
 spositions to generate this cycle\, and that the number of such factorizat
 ions in $n^{n-2}$. We will consider here factorizations into $n-1+2g$ tran
 spositions\, for some fixed $g \\geq 0$\, which we call factorizations of 
 genus $g$. Through bijections with a family of maps\, I will present a co
 mbinatorial construction of a random (almost) uniform factorization of fix
 ed genus\, and an explicit algorithm to sample it. From this\, I will dedu
 ce the scaling limit of a uniform factorization of genus $g$.Joint work wi
 th Valentin Féray and Baptiste Louf.\n\nhttps://indico.math.cnrs.fr/event
 /15781/
LOCATION:Salle de Séminaires (Orléans)
URL:https://indico.math.cnrs.fr/event/15781/
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