论文标题
非 - $ \ ell $ - ABELIAN $ \ ELL $ - 多编码的跨越树木数量的一部分
The non-$\ell$-part of the number of spanning trees in abelian $\ell$-towers of multigraphs
论文作者
论文摘要
让$ \ ell $和$ p $是两个不同的素数。我们研究了Abelian $ \ ell $ the-el $ thecected Multigraphs的$ p $ adiC估值。这类似于华盛顿的古典定理 - sinnott关于cylotomic $ \ mathbb {z} _ \ ell $ - $ \ mathbb {q} $的$ p $ - 部分的增长。此外，我们表明，在某些假设下，将跨越树木的数量分开的数量在这样的塔中是无限的。
Let $\ell$ and $p$ be two distinct primes. We study the $p$-adic valuation of the number of spanning trees in an abelian $\ell$-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 $\mathbb{Z}_\ell$-extension of abelian extensions of $\mathbb{Q}$. Furthermore, we show that under certain hypotheses, the number of primes dividing the number of spanning trees is unbounded in such a tower.
