On abelian $$\ell $$ -towers of multigraphs
Tóm tắt
We study how the
$$\ell $$
-adic valuation of the number of spanning trees varies in regular abelian
$$\ell $$
-towers of multigraphs. We show that for an infinite family of regular abelian
$$\ell $$
-towers of bouquets, the
$$\ell $$
-adic valuation of the number of spanning trees behaves similarly to the
$$\ell $$
-adic valuation of the class numbers in
$${\mathbb {Z}}_{\ell }$$
-extensions of number fields.
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