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English version: Journal of Applied and Industrial Mathematics, 2018, 12:4, 729–737 |
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Volume 25, No 4, 2018, P. 97-111 UDC 519.1
Keywords: set, characteristic function, group, progression, coset. DOI: 10.17377/daio.2018.25.608 Aleksandr A. Sapozhenko 1 Received 29 January 2018 References[1] V. G. Sargsyan, The number of differences in groups of prime order, Diskretn. Mat., 25, No. 1, 152–158, 2013 [Russian]. Translated in Discrete Math. Appl., 23, No. 2, 195–201, 2013.[2] V. G. Sargsyan, Counting sumsets and differences in abelian group, Diskretn. Anal. Issled. Oper., 22, No. 2, 73–85, 2015 [Russian]. [3] A. Alon, Large sets in finite fields are sumsets, J. Number Theory, 126, 110–118, 2007. [4] A. Alon, A. Granville and A. Ubis, The number of sumsets in a finite field, Bull. Lond. Math. Soc., 42, No. 5, 784–794, 2010. [5] E. Croot and V. F. Lev, Open problems in additive combinatorics, in Additive Combinatorics, [6] B. Green, Essay submitted for Smith’s Prize, Camb. Univ., Cambridge, 2001. [7] B. Green and I. Z. Ruzsa, Counting sumsets and sum-free sets modulo a prime, Stud. Sci. Math. Hung., 41, No. 3, 285–293, 2004. [8] B. Green and I. Z. Ruzsa, Sum-free sets in abelian groups, Isr. J. Math., 147, 157–188, 2005. |
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