Resumen de Bijective enumeration of constellations in higher genus

Jordi Castellví

• català

  Bousquet-M´elou i Schaeffer donaren el 2000 una enumeraci´o bijectiva de certs mapes anomenats constel.lacions. El 2019, Lepoutre va descriure una bijecci´o entre mapes biacoloribles de g`enere arbitrari i certs mapes unicel.lulars del mateix g`enere. Presentem una bijecci´o entre constel. lacions de g`enere superior i certs mapes unicellulars que generalitza les dues bijeccions existents alhora. Fent servir aquesta bijecci´o, enumerem una subclasse de constel. lacions sobre el tor, demostrant que llur funci´o generadora ´es una funci´o racional de la funci´o generadora de certs arbres

• English

  Bousquet-M´elou and Schaeffer gave in 2000 a bijective enumeration of some planar maps called constellations. In 2019, Lepoutre described a bijection between bicolorable maps of arbitrary genus and some unicellular maps of the same genus. We present a bijection between constellations of higher genus and some unicellular maps that generalizes both existing bijections at the same time. Using this bijection, we manage to enumerate a subclass of constellations on the torus, proving that its generating function is a rational function of the generating function of some trees