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Preprint · arXiv · December 19, 2025

Enumeration of multipartite series-reduced trees

Medet Jumadildayev
Read on arXivPDFDOI 10.48550/arxiv.2512.17216

Abstract

We obtain a generating function for the degree sequences and colors of rooted multipartite labeled series-reduced trees. As an application of this result, we determine the number of symbolic ultrametrics (introduced by Böcker and Dress) and increasingly labeled processes. We also find that the number of multipartite labeled series-reduced trees and the colored chain-increasing binary trees are the same. We obtain the number of rooted multipartite unlabeled series-reduced trees. We also find a refinement of the result of Riordan and Shannon.

Advanced Combinatorial MathematicsAdvanced Graph Theory ResearchGraph theory and applicationslabeled treesgenerating functionsdegree sequences

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