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SUMMARY:María Ronco (Universidad de Talca)
DTSTART:20200811T213000Z
DTEND:20200811T223000Z
DTSTAMP:20260423T021705Z
UID:operad/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/operad/3/">O
 rder and substitution on graph associahedra</a>\nby María Ronco (Universi
 dad de Talca) as part of operad pop-up\n\n\nAbstract\nM. Carr and S. Devad
 oss introduced in [1] associated a finite partially ordered set to any sim
 ple finite graph\, whose geometric realization is a convex polytope ${\\ma
 thcal K}\\Gamma$\, the graph-associahedron. Their construction include man
 y well-known families of polytopes\, liked permutahedra\, associahedra\, c
 yclohedra and the standard simplexes.\n\nThe goal of the present work is t
 o give an <i>algebraic</i> description of graph associahedra. We introduce
  a substitution operation on Carr and Devadoss tubings\, which allows us t
 o describe graph associahedra as a free object on the set of all connected
  simple graphs\, for a type of colored operad generated by pairs of a fini
 te connected graph and a connected subgraph of it.\n\nWe show that substit
 ution of tubings may be understood in the context of M. Batanin and M. Mar
 kl's operadic categories. We describe an order on the faces of graph-assoc
 iahedra\, different from the one given by Carr and Devadoss\, which allows
  us to construct a standard triangulation of graph associahedra\, followin
 g [2].\n\n(joint work with Stefan Forcey)\n\n[1] M. Carr\, S. Devadoss\, <
 i>Coxeter complexes and graph associahedra</i>\, Topol. and its Applic. 15
 3 (1-2) (2006) 2155–2168.<br/ >\n[2] J.-L. Loday\, <i>Parking functions 
 and triangulation of the associahedron</i>\, Proceedings of the Street’s
  fest 2006\, Contemp. Math. AMS 431 (2007)\, 327–340.\n
LOCATION:https://researchseminars.org/talk/operad/3/
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