Skip to content

Improve lower bound for C_3c #70

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
sebastian-griego wants to merge 1 commit into
base: main
Choose a base branch
from
+4 −2
Open

Improve lower bound for C_3c #70

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
6 changes: 4 additions & 2 deletions constants/3c.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -29,6 +29,7 @@ $$ A \stackrel{G}{\pm} rB := \{ a \pm rb: a \in A, b \in B\}.$$
| $1.61226$ | [L2015] | |
| $1.668$ | [GGSWT2025] | |
| $1.67471$ | [A2026] | |
| $1.67473389$ | [SG2026] | Entropy construction on a 26-point support. |



Expand All @@ -38,13 +39,14 @@ $$ A \stackrel{G}{\pm} rB := \{ a \pm rb: a \in A, b \in B\}.$$
## Additional comments and links


- Has many other formulations [GR2019], including an entropy formulation: $C_{3b}$ is the smallest constant such that for any pair of discrete random variables $X,Y$ one has
$$ H(X-Y) \leq C_{3b} \max( H(X), H(Y), H(X+Y), H(X+2Y)).$$ This entropy formulation has been used to attain all known lower bounds.
- Has many other formulations [GR2019], including an entropy formulation: $C_{3c}$ is the smallest constant such that for any pair of discrete random variables $X,Y$ one has
$$ H(X-Y) \leq C_{3c} \max( H(X), H(Y), H(X+Y), H(X+2Y)).$$ This entropy formulation has been used to attain all known lower bounds.
- Related to the arithmetic Kakeya conjecture [KT2002], [GR2019], which considers other sets of slopes than $0,1,2,\infty$.


## References
- [A2026] Astor, T. Improved Arithmetic Kakeya-Type Counterexamples. TBA (2026)
- [SG2026] Griego, Sebastian. 26-point entropy certificate for $C_{3c}$, submitted to this repository (2026).
- [GGSWT2025] Georgiev, Bogdan; Gómez-Serrano, Javier; Tao, Terence; Wagner, Adam Zsolt. Mathematical exploration and discovery at scale. [arXiv:2511.02864](https://arxiv.org/abs/2511.02864)
- [GR2019] Green, B.; Ruzsa, I. Z. On the arithmetic Kakeya conjecture of Katz and Tao. Periodica Mathematica Hungarica, Volume 78, Issue 1, pp 135–151 (2019). DOI: 10.1007/s10958-018-2003-3.
- [L2015] Lemm, Marius. New counterexamples for sums-differences. Proceedings of the American Mathematical Society, Vol. 143, No. 9 (SEPTEMBER 2015), pp. 3863-3868 (6 pages). DOI: 10.1090/proc/12731.
Expand Down