PreprintCC BY 4.0arXiv
Bouvier's Conjecture and Dimension Sequences of Unique Factorization Domains
Abstract
We prove Bouvier's conjecture. More generally, an integer sequence (an)n ≥ 0 with a0=d ≥ 0 is realized by a unique factorization domain (UFD) R with dim R[X1,…,Xn]=an for every n ≥ 0 if and only if an+1≤ an+1 ≤ an+⌊(an+1)/(n+1)⌋ (n≥0) and a1 ≤ 2d whenever d ≥ 1.
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BibTeX
@misc{tran2026bouviers,
title = {{Bouvier's Conjecture and Dimension Sequences of Unique Factorization Domains}},
author = {Viet-Hoang Tran and Thieu N. Vo and Tan M. Nguyen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01887},
eprint = {2609.01887},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01887},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bouvier's Conjecture and Dimension Sequences of Unique Factorization Domains
AU - Viet-Hoang Tran
AU - Thieu N. Vo
AU - Tan M. Nguyen
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.01887
UR - https://arxiv.org/abs/2609.01887
AB - We prove Bouvier's conjecture. More generally, an integer sequence (a_n)_n ≥ 0 with a_0=d ≥ 0 is realized by a unique factorization domain (UFD) R with dim R[X_1,…,X_n]=a_n for every n ≥ 0 if and only if a_n+1≤ a_n+1 ≤ a_n+⌊(a_n+1)/(n+1)⌋ (n≥0) and a_1 ≤ 2d whenever d ≥ 1.
ER -