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SUMMARY:Solving equations from combinatorics via computer algebra
DTSTART:20260108T093000Z
DTEND:20260108T103000Z
DTSTAMP:20260309T034200Z
UID:indico-event-15833@indico.math.cnrs.fr
DESCRIPTION:Speakers: Hadrien Notarantonio\n\nEnumerative combinatorics co
 ntains a vast landscape of problems that could hardly be solved without th
 e consideration of special functional equations called “Discrete Differe
 ntial Equations”. Among these problems\, the enumeration of walks\, plan
 ar maps carrying physical configurations\, etc. These functional equations
  relate formal power series in n variables with specializations of them to
  some of the variables (the specializations being generating functions rel
 ated to the enumeration of interest). When the involved variables are “n
 ested”\, a celebrated result by Popescu (1986) implies algebraicity of t
 he solutions. In 2006\, Bousquet-Mélou and Jehanne provided an elementary
  proof of algebraicity of the solutions in the case n=2. Their proof yield
 s an algorithm\, and it has been the state-of-the-art in enumerative combi
 natorics for solving these equations since then. In this talk\, I will pre
 sent a recent approach\, based on the intensive use of effective algebraic
  geometry\, in order to solve more efficiently such equations in the case 
 n=2. Also\, I will introduce and discuss recent advances in the case of sy
 stems of such equations. The talk is based on joint works with Alin Bostan
 \, Mohab Safey El Din\, Sergey Yurkevich and Mireille Bousquet-Mélou.\n\n
 https://indico.math.cnrs.fr/event/15833/
LOCATION:Visio
URL:https://indico.math.cnrs.fr/event/15833/
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