论文标题
在$ \ mathbb {z} _ {\ ell}^{d} $ - 图形塔
On $\mathbb{Z}_{\ell}^{d}$-towers of graphs
论文作者
论文摘要
令$ \ ell $为理性的素数。我们表明，图理论中格林伯格猜想的类似物是正确的。更确切地说，我们表明，如果$ n $足够大，则$ \ n $ the $ n $ the层的$ \ ell $ - ad $ - adbb {z} _ {\ ell}^{d}^{d} $ - themial in $ \ ell^n $ n $ n $ n $ n $ n $ n $ n $ n $ n polotice and coeff and $和n $ n $ n $ n $ n。 $ n $的学位最多。
Let $\ell$ be a rational prime. We show that an analogue of a conjecture of Greenberg in graph theory holds true. More precisely, we show that when $n$ is sufficiently large, the $\ell$-adic valuation of the number of spanning trees at the $n$th layer of a $\mathbb{Z}_{\ell}^{d}$-tower of graphs is given by a polynomial in $\ell^{n}$ and $n$ with rational coefficients of total degree at most $d$ and of degree in $n$ at most one.
