3^n

Xavier Gérard Viennot (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We revisit some old problems of directed animals and compact source animals on a square lattice, whose number was found to be 3^n, and recent extensions with multidirected animals. The connection of such problems with Lorentzian quantum gravity will be discussed. A bijective proof (that we call the "Nordic decomposition" of a heap of dimers) for the formula for multidirected animals, which at the same time give some extensions for Lorentzian triangulations, will be presented. Besides physicists, the topic should be of interest to computer scientists. For computer scientists, we use the model of heaps of pieces, which is equivalent to the concept of trace in computer science, used as model for concurrency access to data structures. The bijective problems show some philosophical considerations about algorithmic constructions of bijections which have a computer science flavor.

Domaines: Combinatoire [math.CO]; Mécanique statistique [cond-mat.stat-mech]

Xavier Gérard Viennot. 3^n. Colloquium de Physique Théorique, TIFR (Tata Institute of Fundamental Research) Bombay, Feb 2013, Mumbai, India. ⟨hal-00998331⟩