Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T13:00:39.545Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the polynomial Freĭman–Ruzsa conjecture over ℤ

Published online by Cambridge University Press:  10 November 2017

FREDDIE MANNERS
FREDDIE MANNERS*
Affiliation:
450 Serra Mall Building 380, Stanford 94305, U.S.A. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The polynomial Freĭman–Ruzsa conjecture over the integers is often phrased in terms of convex progressions. We give an alternative, apparently stronger formulation in terms of the more restrictive “ellipsoid progressions”, and show that these formulations are in fact equivalent. The key input to the equivalence proof comes from strong results in asymptotic convex geometry.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 166 , Issue 2 , March 2019 , pp. 243 - 245
Copyright
Copyright © Cambridge Philosophical Society 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[GM04] Giannopoulos, A. A. and Milman, V. D. Asymptotic convex geometry: short overview. In Different faces of geometry Int. Math. Ser. (N. Y.) vol. 3 (Kluwer/Plenum, New York, 2004), pages 87–162.Google Scholar
[Gre07] Green, B. The polynomial Freĭman–Ruzsa conjecture. Terence Tao's blog (2007).Google Scholar
[LR17] Lovett, S. and Regev, O. A counterexample to a strong variant of the polynomial Freiman–Ruzsa conjecture in Euclidean space. Discrete Anal., pages Paper No. 8, 6 (2017).Google Scholar
[Mil86] Milman, V. D. Inégalité de Brunn–Minkowski inverse et applications à la théorie locale des espaces normés. C. R. Acad. Sci. Paris Sér. I Math. 302 (1) (1986), 25–28.Google Scholar