Regular colored graphs of positive degree

• Verfasst von: Gurǎu, Rǎzvan [VerfasserIn]
• Verfasst von: Schaeffer, Gilles [VerfasserIn]
• Titel: Regular colored graphs of positive degree
• Verf.angabe: Razvan Gurau and Gilles Schaeffer
• Ausgabe: Version v3
• E-Jahr: 2016
• Jahr: 1 Feb 2016
• Jahr des Originals: 2013
• Umfang: 45 S.
• Fussnoten: Version 1 vom 19. Juli 2013, Version 3 vom 1. Februar 2016 ; Gesehen am 05.10.2022
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2016
• Band/Heft Quelle: (2016), Artikel-ID 1307.5279, Seite 1-45
• DOI: doi:10.48550/arXiv.1307.5279
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 05C30, 81T18
• Sach-SW: Mathematical Physics
• Sach-SW: Mathematics - Combinatorics
• K10plus-PPN: 1805158082

Abstract

Regular colored graphs are dual representations of pure colored D-dimensional complexes. These graphs can be classified with respect to an integer, their degree, much like maps are characterized by the genus. We analyse the structure of regular colored graphs of fixed positive degree and perform their exact and asymptotic enumeration. In particular we show that the generating function of the family of graphs of fixed degree is an algebraic series with a positive radius of convergence, independant of the degree. We describe the singular behavior of this series near its dominant singularity, and use the results to establish the double scaling limit of colored tensor models.