Quantitative concatenation for polynomial box norms
Year: 2026
Type: article
Abstract: Using PET and quantitative concatenation techniques, we establish box-norm control with the "expected" directions for counting operators for general multidimensional polynomial progressions, with at most polynomial losses in the parameters. Such results are often useful first steps towards obtaining explicit upper bounds on sets lacking instances of given such progressions. In the companion paper arXiv:2407.08637, we complete this program for sets in $[N]^2$ lacking nondegenerate progressions of the form $(x, y), (x + P(z), y), (x, y + P(z))$, where $P \in \mathbb{Z}[z]$ is any fixed polynomial with an integer root of multiplicity $1$.
Source: Advances in Mathematics
Authors: Noah Kravitz, Borys Kuca, James Leng
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,790
OpenAlex ID: W7125964477