Journée-séminaire de combinatoire

(équipe CALIN du LIPN, université Paris-Nord, Villetaneuse)

Le 24 janvier 2023 à 14h00 en B107 & visioconférence, Lionel Pournin nous parlera de : Distance, strong convexity, flagness, and associahedra

Résumé : One can always transform a triangulation of a convex polygon into another by performing a sequence of edge flips, which amounts to follow a path in the graph G of the associahedron. The least number of flips required to do so is then a distance in that graph whose estimation is instrumental in a variety of contexts, as for instance in computational biology, in computer science, or in algebraic topology. On the other hand, it is known that paths in G correspond to a certain kind of 3-dimensional triangulation. This talk is about the recent proof that these 3-dimensional triangulations are flag when the corresponding path is a geodesic. This result, that provides a new powerful tool to study the geometry of G, can be thought of as a 3-dimensional analogue of a well-known strong convexity property of G. Several consequences on the computation of distances in G and on strong convexity in related graphs will be discussed. This talk is based on joint work with Zili Wang (Dartmouth College).


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