2022/01/13 by Antonio Lei, Lei, Antonio, Daniel Vallières +1
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2201.05186
openalex publication_date 2022/01/13 · openalex created_date 2023/02/19 · openalex updated_date 2026/07/28
Let ℓ and p be two distinct primes. We study the p-adic valuation of the number of spanning trees in an abelian ℓ-tower of connected multigraphs. This is analogous to the classical theorem of Washington--Sinnott on the growth of the p-part of the class group in a cyclotomic ℤ_ℓ-extension of abelian extensions of ℚ. Furthermore, we show that under certain hypotheses, the number of primes dividing the number of spanning trees is unbounded in such a tower.