Enumeration of tree-type diagrams assembled from oriented chains of edges

O. Khorunzhiy

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arXiv · 2207.00766

Enumeration of tree-type diagrams assembled from oriented chains of edges

O. Khorunzhiy

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Abstract

We study a family of tree-type diagrams that arise in studies of the cumulant expansion in discrete Erd\H os-R\'enyi 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 Pr\"ufer 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.

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O. Khorunzhiy. 2022-07-02. Enumeration of tree-type diagrams assembled from oriented chains of edges. https://arxiv.org/abs/2207.00766

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