图的塔

Q3 Mathematics

Algebraic Combinatorics Pub Date : 2023-11-07 DOI:10.5802/alco.304

Sage DuBose, Daniel Vallières

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引用次数: 0

摘要

设l是有理数。我们证明了图论中格林伯格猜想的一个类比是正确的。更确切地说，我们证明了当n足够大时，在nn和n上的一个多项式给出了n层生成树数目的n进值，其总度数最多为d, n上的度数最多为1。

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On ℤ ℓ d -towers of graphs

Let ℓ 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 ℓ-adic valuation of the number of spanning trees at the nth layer of a ℤ ℓ d -tower of graphs is given by a polynomial in ℓ n and n with rational coefficients of total degree at most d and of degree in n at most one.

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来源期刊

Algebraic Combinatorics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

51 weeks