From 08355b6a829358e7991a92d84340c24b5435d9f0 Mon Sep 17 00:00:00 2001 From: Taksh Date: Sun, 28 Jun 2026 20:44:37 +0530 Subject: [PATCH] fix: restore LaTeX subscripts on Marton constant page PR #98 escaped underscores inside math mode, breaking F_2 rendering. Co-authored-by: Cursor --- constants/18a.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/constants/18a.md b/constants/18a.md index d1cbd3f..95d4b36 100644 --- a/constants/18a.md +++ b/constants/18a.md @@ -2,7 +2,7 @@ ## Description of constant -$C_{18}$ is the least constant such that, whenever $A$ is a subset of $\mathbb F\_{2}^n$ with $\lvert A+A\rvert \leq K\lvert A\rvert$, then $A$ can be covered by $K^{C_{18}+o(1)}$ cosets of a subspace of cardinality at most $\lvert A\rvert$, where the limit $o(1)$ is with respect to the limit $K \to \infty$. +$C_{18}$ is the least constant such that, whenever $A$ is a subset of $\mathbb F_2^n$ with $\lvert A+A\rvert \leq K\lvert A\rvert$, then $A$ can be covered by $K^{C_{18}+o(1)}$ cosets of a subspace of cardinality at most $\lvert A\rvert$, where the limit $o(1)$ is with respect to the limit $K \to \infty$. ## Known upper bounds @@ -19,7 +19,7 @@ $C_{18}$ is the least constant such that, whenever $A$ is a subset of $\mathbb F ## Additional comments and links -- Conjectured to be finite by Katalin Marton, as recorded in [R1999]. It is the special case of the Polynomial Freiman-Ruzsa (PFR) conjecture when the ambient group is a vector space over the field $\mathbb F\_{2}$. (The precise formulation of the PFR conjecture in the case of unbounded torsion is still not fully settled.) +- Conjectured to be finite by Katalin Marton, as recorded in [R1999]. It is the special case of the Polynomial Freiman-Ruzsa (PFR) conjecture when the ambient group is a vector space over the field $\mathbb F_2$. (The precise formulation of the PFR conjecture in the case of unbounded torsion is still not fully settled.) - The lower bound of 1 is not expected to be sharp. - Surveys on this problem can be found at [G2005], [G-unpub], and [Lovett2015]. @@ -29,5 +29,5 @@ $C_{18}$ is the least constant such that, whenever $A$ is a subset of $\mathbb F - [G-unpub] Green, B. J. *Notes on the polynomial Freiman–Ruzsa conjecture.* Unpublished note available at https://people.maths.ox.ac.uk/greenbj/papers/PFR.pdf - [GGMT2025] Gowers, W. T.; Green, B.; Manners, F.; Tao, T. *On a conjecture of Marton.* Annals of Mathematics, Second Series, Volume 201 (2025), Issue 2, 515–549. [arXiv:2311.05762](https://arxiv.org/abs/2311.05762) - [Lovett2015] Lovett, S. *An Exposition of Sanders’ Quasi-Polynomial Freiman–Ruzsa Theorem.* Theory of Computing Library Graduate Surveys 6 (2015), 1–14. -- [L2024] Liao, J.-J. *Improved Exponent for Marton's Conjecture in $\mathbb F\_{2}^n$.* [arXiv:2404.09639](https://arxiv.org/abs/2404.09639) (2024). +- [L2024] Liao, J.-J. *Improved Exponent for Marton's Conjecture in $\mathbb F_2^n$.* [arXiv:2404.09639](https://arxiv.org/abs/2404.09639) (2024). - [R1999] Ruzsa, I. Z. *An analog of Freiman’s theorem in groups.* Astérisque 258 (1999), 323–326. \ No newline at end of file