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Let 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 is sufficiently large, the -adic valuation of the number of spanning trees at the th layer of a -tower of graphs is given by a polynomial in and with rational coefficients of total degree at most and of degree in at most one.
DuBose, Sage 1 ; Vallières, Daniel 1
CC-BY 4.0
@article{ALCO_2023__6_5_1331_0,
author = {DuBose, Sage and Valli\`eres, Daniel},
title = {On $\mathbb{Z}_{\ell }^{d}$-towers of graphs},
journal = {Algebraic Combinatorics},
pages = {1331--1346},
publisher = {The Combinatorics Consortium},
volume = {6},
number = {5},
year = {2023},
doi = {10.5802/alco.304},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/alco.304/}
}
TY - JOUR
AU - DuBose, Sage
AU - Vallières, Daniel
TI - On $\mathbb{Z}_{\ell }^{d}$-towers of graphs
JO - Algebraic Combinatorics
PY - 2023
SP - 1331
EP - 1346
VL - 6
IS - 5
PB - The Combinatorics Consortium
UR - http://geodesic.mathdoc.fr/articles/10.5802/alco.304/
DO - 10.5802/alco.304
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ID - ALCO_2023__6_5_1331_0
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%A Vallières, Daniel
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%D 2023
%P 1331-1346
%V 6
%N 5
%I The Combinatorics Consortium
%U http://geodesic.mathdoc.fr/articles/10.5802/alco.304/
%R 10.5802/alco.304
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DuBose, Sage; Vallières, Daniel. On $\mathbb{Z}_{\ell }^{d}$-towers of graphs. Algebraic Combinatorics, Tome 6 (2023) no. 5, pp. 1331-1346. doi: 10.5802/alco.304
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