Bounds on the size of Progression-Free Sets in ℤ_mⁿ

[1] BATEMAN, M.—KATZ, N. H.: New bounds on cap sets, J.Amer. Math.Soc. 25 (2012), no. 2, 585–613. Search in Google Scholar

[2] BLASIAK, J. — CHURCH, T. — COHN, H. — GROCHOW, J. — NASLUND, E. – SAWIN, W. — UMANS, C.: On cap sets and the group-theoretic approach to matrix multiplication, Discrete Anal. 2017, art. no. 3, 27 pp.10.19086/da.1245 Search in Google Scholar

[3] BROWN, T. C.—BUHLER, J. P.: A density version of a geometric Ramsey theorem, J. Combin. Theory Ser. A 25 (1982), 20–34.10.1016/0097-3165(82)90062-0 Search in Google Scholar

[4] CROOT, E.—LEV, V. F.—PACH, P. P.: Progression-free sets in ℤⁿ₄ are exponentially small, Ann. of Math. (2) 185 (2017), no. 1, 331–337. Search in Google Scholar

[5] EDEL, Y.: Extensions of generalized product caps, Des. Codes Cryptogr. 31 (2004), 5–14.10.1023/A:1027365901231 Search in Google Scholar

[6] EDEL, Y.—FERRET, S.—LANDJEV, I.—STORME, L.: The classification of the largest caps in AG(5, 3), J. Combin. Theory Ser. A 99 (2002), 95–110.10.1006/jcta.2002.3261 Search in Google Scholar

[7] ELLENBERG, J. S.—GIJSWIJT, D.: On large subsets of 𝔽ⁿ_q with no three-term arithmetic progression, Ann. of Math. (2) 185 (2017), no. 1, 339–343. Search in Google Scholar

[8] ELSHOLTZ, C.—PACH, P. P.: Caps and progression-free sets in ℤⁿ_m,Des.Codes Cryptogr. 88 (2020), 2133–2170.10.1007/s10623-020-00769-0752733733071461 Search in Google Scholar

[9] FRANKL, P.—GRAHAM, R. L.—RÖDL, V.: On subsets of abelian groups with no 3--term arithmetic progression, J. Combin. Theory, Ser. A 45 (1987), no. 1, 157–161. Search in Google Scholar

[10] LEV, V. F.: Progression-free sets in finite abelian groups, J. Number Theory 104 (2004), 162–169.10.1016/S0022-314X(03)00148-3 Search in Google Scholar

[11] MESHULAM, R.: On subsets of finite abelian groups with no 3-term arithmetic progressions,J.Comb. Theory, Ser.A 71 (1995), 168–172. Search in Google Scholar

[12] PACH, P. P.—PALINCZA, R.: Sets avoiding six-term arithmetic progressions in ℤⁿ₆ are exponentially small, SIAM Journal Discrete Math. (to appear) Search in Google Scholar

[13] PETROV, F.: Combinatorial results implied by many zero divisors in a group ring; https://doi.org/10.48550/arXiv.1606.03256 Search in Google Scholar

[14] PETROV, F.—POHOATA, C.: Improved Bounds for Progression-Free Sets in Cⁿ₈,Israel J. Math. 236 (2020), no. 1, 345–363. Search in Google Scholar

[15] POTECHIN, A.: Maximal caps in AG(6, 3), Des. Codes Cryptogr. 46 (2008), no. 3, 243–259. Search in Google Scholar

[16] SANDERS, T.: Roth’s theorem in ℤⁿ₄,Anal. PDE 2 (2009), no. 2, 211–234. Search in Google Scholar

[17] SPEYER, D.: Bounds for sum free sets in prime power cyclic groups — three ways; https://sbseminar.wordpress.com/2016/07/08/bounds-for-sum-free-sets-inprime--power-cyclic-groups-three-ways Search in Google Scholar

[18] SAWIN, W.—TAO, T.: Notes on the slice rank of tensors, (2016); https://terrytao.wordpress.com/2016/08/24/notes-on-the-slice-rank-of-tensors Search in Google Scholar

[19] TAO, T.: A symmetric formulation of the Croot-Lev-Pach-Ellenberg-Gijswijt capset bound, (2016); https://terrytao.wordpress.com/2016/05/18/a-symmetric-formulation-of-the--croot-lev-pach-ellenberg-gijswijt-capset-bound Search in Google Scholar