On the number of planar Eulerian orientations
| Autor: | Claire Pennarun, Mireille Bousquet-Mélou, Paul Dorbec, Nicolas Bonichon |
|---|---|
| Přispěvatelé: | Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), Centre National de la Recherche Scientifique (CNRS), ANR-12-JS02-0002,EGOS,Graphes Plongés et leurs Structures Orientées(2012), ANR-14-CE25-0014,GRAAL,GRaphes et Arbres ALéatoires(2014) |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Polynomial
Series (mathematics) 010102 general mathematics System of polynomial equations Eulerian path 0102 computer and information sciences 01 natural sciences Combinatorics symbols.namesake Integer 010201 computation theory & mathematics Simple (abstract algebra) generating functions Eulerian orientations [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] symbols FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Combinatorics (math.CO) 0101 mathematics Algebraic number Divided differences planar maps Mathematics |
| Zdroj: | European Journal of Combinatorics European Journal of Combinatorics, Elsevier, 2017, 65, pp.59-91 HAL |
| ISSN: | 0195-6698 1095-9971 |
| Popis: | The number of planar Eulerian maps with n edges is well-known to have a simple expression. But what is the number of planar Eulerian orientations with n edges? This problem appears to be a difficult one. To approach it, we define and count families of subsets and supersets of planar Eulerian orientations, indexed by an integer k , that converge to the set of all planar Eulerian orientations as k increases. The generating functions of our subsets can be characterized by systems of polynomial equations, and are thus algebraic. The generating functions of our supersets are characterized by polynomial systems involving divided differences, as often occurs in map enumeration. We prove that these series are algebraic as well. We obtain in this way lower and upper bounds on the growth rate of planar Eulerian orientations, which appears to be around 12.5. |
| Databáze: | OpenAIRE |
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