Fetching the paper…
Reading the bibliography…
We prove a Freiman--Ruzsa-type theorem with polynomial bounds in arbitrary abelian groups with bounded torsion, thereby proving (in full generality) a conjecture of Marton.
H. Plünnecke, Eine zahlentheoretische anwendung der graphtheorie , J. Reine Angew. Math. 243
1970
Earlier work this paper cites.
V. A. Kaimanovich and A. M. Vershik, Random walks on discrete groups: boundary and entropy , Ann. Probab. 11
1983
Earlier work this paper cites.
I. Z. Ruzsa, An application of graph theory to additive number theory , Sci. Ser. A Math. Sci. (N.S.) 3
1989
Earlier work this paper cites.
T. C. Tao and V. Vu, Additive combinatorics, Cambridge Stud. Adv. Math., 105 Cambridge University Press, Cambridge, 2006, xviii+512 pp
2006
Earlier work this paper cites.
A. Samorodnitsky, Low-degree tests at large distances, In Proceedings of the thirty-ninth annual ACM symposium on Theory of computing, 2007, 506–515
2007
Earlier work this paper cites.
B. Bukh, Sums of dilates , Comb. Probab. Comput. 17
2008
Earlier work this paper cites.
B. J. Green and T. C. Tao, An inverse theorem for the Gowers U 3 ( G ) U^{3}(G) -norm , Proc. Edinb. Math. Soc. 51
2008
Cited alongside, same era.
M. Madiman, On the entropy of sums , in Information Theory Workshop 2008. ITW ’08. IEEE: 303–307, 2008
2008
Cited alongside, same era.
I. Z. Ruzsa, Sumsets and entropy, Random Struct. Alg., 34
2009
Cited alongside, same era.
B. J. Green and T. C. Tao, An equivalence between inverse sumset theorems and inverse conjectures for the U 3 U^{3} norm , Math. Proc. Cambridge Philos. Soc. 149
2010
Cited alongside, same era.
T. C. Tao, Sumset and inverse sumset theory for Shannon entropy , Combin. Probab. Comput. 19
2010
Cited alongside, same era.
S. Lovett, Equivalence of polynomial conjectures in additive combinatorics , Combinatorica 32
2012
Later among the works it cites.
G. Petridis, New proofs of Plünnecke-type estimates for product sets in groups , Combinatorica 32
2012
Later among the works it cites.
T. Sanders, On the Bogolyubov–Ruzsa lemma , Anal. PDE 5
2012
Later among the works it cites.
T. Sanders, The structure theory of set addition revisited, Bull. Amer. Math. Soc. 50
2013
Later among the works it cites.
B. Hanson, G. Petridis, A question of Bukh on sums of dilates , Discrete Anal. 2021
2021
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited in the paper.
Cited in the paper.