PreprintCC BY 4.0arXiv
Minimal asymptotic g-adic bases from arbitrary partitions
Abstract
Let g>h≥2 be integers. For a nonempty set W⊆N, let ℱ*(W) denote the set of its finite nonempty subsets. Let Ag(W)={∑f∈ Fafgf: 1≤ af ≤ g−1,F ∈ ℱ*(W)}, and let N=W1sqcup⋯sqcup Wh be a partition into infinite sets. We prove that A=⋃i=1h Ag(Wi) is a minimal asymptotic basis of order h for every such partition.
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BibTeX
@misc{tang2026minimal,
title = {{Minimal asymptotic \(g\)-adic bases from arbitrary partitions}},
author = {Min Tang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23152},
eprint = {2610.23152},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23152},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Minimal asymptotic g-adic bases from arbitrary partitions
AU - Min Tang
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23152
UR - https://arxiv.org/abs/2610.23152
AB - Let g>h≥2 be integers. For a nonempty set W⊆N, let ℱ^*(W) denote the set of its finite nonempty subsets. Let A_g(W)={∑_f∈ Fa_fg^f: 1≤ a_f ≤ g−1,F ∈ ℱ^*(W)}, and let N=W_1sqcup⋯sqcup W_h be a partition into infinite sets. We prove that A=⋃_i=1^h A_g(W_i) is a minimal asymptotic basis of order h for every such partition.
ER -