A bijection for tricellular maps
type: Item
instance of: scholarly article
title: A bijection for tricellular maps
zbMATH Open document ID: 1408.05016
DOI: 10.1155/2013/712431
author: Hillary S. W. Han
author: Christian M. Reidys
published in: ISRN Discrete Mathematics
publication date: 2014-11-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1305.3460
review text: Summary: We give a bijective proof for a relation between unicellular, bicellular, and tricellular maps. These maps represent cell complexes of orientable surfaces having one, two, or three boundary components. The relation can formally be obtained using matrix theory employing the Schwinger-Dyson equation. In this paper we present a bijective proof of the corresponding coefficient equation. Our result is a bijection that transforms a unicellular map of genus \(g\) into unicellular, bicellular or tricellular maps of strictly lower genera. The bijection employs edge cutting, edge contraction, and edge deletion.
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A10
Mathematics Subject Classification ID: 05C30
zbMATH DE Number: 6368844
zbMATH Keywords: polygon gluings
zbMATH Keywords: bijection
zbMATH Keywords: Harer-Zagier numbers
Wikidata QID: Q56266982
MaRDI profile type: Publication
OpenAlex ID: W1991708965
arXiv ID: 1305.3460
cites work: Spaces of RNA secondary structures
cites work: The decorated Teichmüller space of punctured surfaces
cites work: The chromatic polynomial of fatgraphs and its categorification
cites work: The Euler characteristic of the moduli space of curves
cites work: Perturbative series and the moduli space of Riemann surfaces
cites work: A new combinatorial identity for unicellular maps, via a direct bijective approach
cites work: The S Matrix in Quantum Electrodynamics
cites work: Q5808247
cites work: Q4890772
cites work: Combinatorics of RNA-RNA interaction
description: scientific article; zbMATH DE number 6368844