Combinatorics Probability Computing· 2026Q1
Low-complexity approximations for sets defined by generalizations of affine conditions
- 1citations
- Q1SCImago
- 2026year
Short summary
A new theorem proves that any set defined by a generalization of affine conditions can be approximated by a simpler structure, with the approximation quality depending on the prime modulus and an error parameter.
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Key points
- A theorem establishes that sets defined by generalized affine conditions in F_p^n can be approximated by simpler structures.
- The approximation quality is bounded by a constant C(p, epsilon), dependent on the prime modulus p and error parameter epsilon.
- This result applies to any positive integer k, representing the number of linear forms defining the set.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract Let p p $p$ be a prime, let upper S S $S$ be a non-empty subset of double struck upper F Subscript p F p $\mathbb{F}_p$ and let 0 less than epsilon less than or equals 1 0 < ϵ ≤ 1 $0\lt \epsilon \leq 1$ . We show that there exists a constant upper C equals upper C left parenthesis p comma epsilon right parenthesis C = C ( p , ϵ ) $C=C(p, \epsilon )$ such that for every positive integer k k $k$ , whenever phi 1 comma ellipsis comma phi Subscript k Baseline colon double struck upper F Subscript p Superscript n Baseline right arrow double struck upper F Subscript p Baseline ϕ 1 , … , ϕ k : F p n → F p $\phi _1, \dots , \phi _k: \mathbb{F}_p^n \rightarrow \mathbb{F}_p$ are linear forms and upper E 1 comma ellipsis comma upper E Subscript k Baseline
The authors' abstract, as published at the source. Combinatorics Probability Computing, 2026 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics