Counting line-colored d-ary trees
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 ve...
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| Main Authors: | , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
19 Jun 2012
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| In: |
Arxiv
Year: 2012, Pages: 1-6 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1206.4203
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| Author Notes: | Valentin Bonzom and Razvan Gurau |
| Summary: | 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 $\frac{1}{\sum_{i=1}^D p_i +1} \binom{\sum_{i=1}^D p_i+1}{p_1} ... \binom{\sum_{i=1}^D p_i+1}{p_D}$. |
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| Item Description: | Gesehen am 05.10.2022 Identifizierung der Ressource nach: November 18, 2018 |
| Physical Description: | Online Resource |