On abelian ℓ-towers of multigraphs

2020/06/24 by Daniel Vallières, Vallières, Daniel
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2006.14012

openalex publication_date 2020/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study how the ℓ-adic valuation of the number of spanning trees varies in regular abelian ℓ-towers of multigraphs. We show that for an infinite family of regular abelian ℓ-towers of bouquets, the behavior of the ℓ-adic valuation of the number of spanning trees behave similarly to the ℓ-adic valuation of the class numbers in ℤ_ℓ-extensions of number fields.

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