Énumération des cartes pointées sur une surface orientable de genre quelconque en fonction des nombres de sommets et de faces
نویسندگان
چکیده
Dans cet article, nous explicitons la forme ge ne rale des se ries ge ne ratrices des cartes pointe es sur une surface orientable, e nume re es en fonction des nombres de sommets et de faces. Toutes ces se ries ge ne ratrices sont des se ries rationnelles d'un unique syste me parame trique des variables de nombrant les sommets et les faces. Nous explicitons ces se ries dans le cas des cartes pointe es de genre 0, 1, 2 et 3. Les solutions pour les genres 2 et 3 sont deux re sultats nouveaux sur les cartes. De plus, la forme ge ne rale propose e pour ces se ries pre cise celle de E. A. Bender et al., en re pondant notamment a une question laisse e ouverte dans deux articles de ces auteurs. We give here general formulas for the generating functions counting rooted maps on an orientable surface by number of vertices and faces. All these generating functions appear to be rational functions of the same parametric system of the variables counting the number of vertices and faces. We make explicit these functions for rooted maps of genus 0, 1, 2, and 3. The solutions for genus 2 and 3 are new results about maps. Moreover, our general formulas refine these of E. A. Bender et al., answering a question left open in their articles on this subject. 1999 Academic Press
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عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 77 شماره
صفحات -
تاریخ انتشار 1999