Year: 2026
Type: preprint
Abstract: We prove Bouvier's conjecture. More generally, an integer sequence $(a_n)_{n \ge 0}$ with $a_0=d \ge 0$ is realized by a unique factorization domain (UFD) $R$ with $\dim R[X_1,\ldots,X_n]=a_n$ for every $n \ge 0$ if and only if $$ a_n+1\le a_{n+1} \le a_n+\left\lfloor\frac{a_n+1}{n+1}\right\rfloor \qquad(n\ge0) $$ and $a_1 \le 2d$ whenever $d \ge 1$.
Source: arXiv (Cornell University)
Authors: Tran, Viet-Hoang, Vo, Thieu N., Nguyen, Tan M.
Institutions: National University of Singapore, University of Bath
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7207565289
Cites:
Cited by:
Related to: