Enumeration of tree-type diagrams assembled from oriented chains of edges
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866910743581949952 |
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| author | Khorunzhiy, O. |
| author_facet | Khorunzhiy, O. |
| contents | We study a family of tree-type diagrams that arise in studies of the cumulant expansion in discrete Erd\H os-Rényi random matrix models. Using a version of the Pr\" ufer code, we obtain an explicit expression for the number of tree-type diagrams assembled from $k$ oriented chains of $q$ edges. Using this modified Prüfer codification, we get an explicit expression for sum overs weighted tree-type diagrams with a weight depending on multiplicity of edges. We describe similar results for tree-type diagrams assembled from chains that are not necessarily regular. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2207_00766 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Enumeration of tree-type diagrams assembled from oriented chains of edges Khorunzhiy, O. Combinatorics Mathematical Physics Probability 05A15, 05C30, 60B20 We study a family of tree-type diagrams that arise in studies of the cumulant expansion in discrete Erd\H os-Rényi random matrix models. Using a version of the Pr\" ufer code, we obtain an explicit expression for the number of tree-type diagrams assembled from $k$ oriented chains of $q$ edges. Using this modified Prüfer codification, we get an explicit expression for sum overs weighted tree-type diagrams with a weight depending on multiplicity of edges. We describe similar results for tree-type diagrams assembled from chains that are not necessarily regular. |
| title | Enumeration of tree-type diagrams assembled from oriented chains of edges |
| topic | Combinatorics Mathematical Physics Probability 05A15, 05C30, 60B20 |
| url | https://arxiv.org/abs/2207.00766 |