Counting line-colored d-ary trees

• Verfasst von: Bonzom, Valentin [VerfasserIn]
• Verfasst von: Gurǎu, Rǎzvan [VerfasserIn]
• Titel: Counting line-colored d-ary trees
• Verf.angabe: Valentin Bonzom and Razvan Gurau
• E-Jahr: 2012
• Jahr: 19 Jun 2012
• Umfang: 6 S.
• Fussnoten: Gesehen am 05.10.2022 ; Identifizierung der Ressource nach: November 18, 2018
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2012
• Band/Heft Quelle: (2012), Artikel-ID 1206.4203, Seite 1-6
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: High Energy Physics - Theory
• Sach-SW: Mathematical Physics
• Sach-SW: Mathematics - Combinatorics
• K10plus-PPN: 1805172069

Abstract

Random tensor models are generalizations of matrix models which also support a 1/N expansion. The dominant observables are in correspondence with some trees, namely rooted trees with vertices of degree at most $D$ and lines colored by a number $i$ from 1 to $D$ such that no two lines connecting a vertex to its descendants have the same color. In this Letter we study by independent methods a generating function for these observables. We prove that the number of such trees with exactly $p_i$ lines of color $i$ is $\frac{1}{\sum_{i=1}^D p_i +1} \binom{\sum_{i=1}^D p_i+1}{p_1} ... \binom{\sum_{i=1}^D p_i+1}{p_D}$.