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Unified bijections for planar hypermaps with general cycle-length constraints
- Source :
- Annales de l’Institut Henri Poincaré D. 7:75-164
- Publication Year :
- 2020
- Publisher :
- European Mathematical Society - EMS - Publishing House GmbH, 2020.
-
Abstract
- We present a general bijective approach to planar hypermaps with two main results. First we obtain unified bijections for all classes of maps or hypermaps defined by face-degree constraints and girth constraints. To any such class we associate bijectively a class of plane trees characterized by local constraints. This unifies and greatly generalizes several bijections for maps and hypermaps. Second, we present yet another level of generalization of the bijective approach by considering classes of maps with non-uniform girth constraints. More precisely, we consider \emph{well-charged maps}, which are maps with an assignment of ''charges'' (real numbers) on vertices and faces, with the constraints that the length of any cycle of the map is at least equal to the sum of the charges of the vertices and faces enclosed by the cycle. We obtain a bijection between charged hypermaps and a class of plane trees characterized by local constraints.
- Subjects :
- Statistics and Probability
Class (set theory)
Generalization
0102 computer and information sciences
01 natural sciences
Combinatorics
Planar
FOS: Mathematics
Mathematics - Combinatorics
Discrete Mathematics and Combinatorics
0101 mathematics
Real number
Mathematics
Mathematics::Combinatorics
Algebra and Number Theory
Plane (geometry)
Probability (math.PR)
010102 general mathematics
Statistical and Nonlinear Physics
Girth (graph theory)
010201 computation theory & mathematics
Bijection
Combinatorics (math.CO)
Geometry and Topology
Bijection, injection and surjection
Mathematics - Probability
Subjects
Details
- ISSN :
- 23085827
- Volume :
- 7
- Database :
- OpenAIRE
- Journal :
- Annales de l’Institut Henri Poincaré D
- Accession number :
- edsair.doi.dedup.....37679ed5c367a1af56b78f17691119ad