Keywords and phrases: abelian groups, inverse problems, subset sums, zero-sum free set.
Received: October 2, 2022; Accepted: November 9, 2022; Published: November 11, 2022
How to cite this article: Mingrui Wang and Yuting Hu, Inverse problems of subset sums of zero-sum free set with six elements in finite abelian groups, JP Journal of Algebra, Number Theory and Applications 59 (2022), 17-31. http://dx.doi.org/10.17654/0972555522036
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] G. Bhowmik, I. Halupczok and J. C. Schlage-Puchta, Zero-sum free sequences with small sum-set, Math. Comp. 80 (2011), 2253-2258. [2] R. B. Eggleton and P. Erdős, Two combinatorial problems in group theory, Scientific paper 117, Dept. of Math., Stat. and Comp. Sci., U. of Calgary, 1971. [3] É. Balandraud, B. Girard, S. Griffiths and Y. Hamidoune, Subset sums in abelian groups, European J. Combin. 34 (2013), 1269-1286. [4] R. B. Eggleton and P. Erdős, Two combinatorial problems in group theory, Acta Arith. 21 (1972), 111-116. [5] L. Chen, G. Li, Y. Wen, H. Yang, J. Liu and J. Peng, On the inverse problems of subsums of zero-sum free subsets, JP Journal of Algebra, Number Theory and Applications 41(1) (2019), 19-33. [6] M. Freeze, W. Gao and A. Geroldinger, The critical number of finite abelian groups, J. Number Theory 129 (2009), 2766-2777. [7] W. Gao and A. Geroldinger, On the structure of zerofree sequences, Combinatorica 18 (1998), 519-527. [8] W. Gao and A. Geroldinger, Zero-sum problems in finite abelian groups: a survey, Egpo. Math. 24 (2006), 337-369. [9] W. Gao, M. Huang, W. Hui, Y. Li, C. Liu and J. Peng, Sums of sets of abelian group elements, J. Number Theory 208 (2020), 208-229. [10] W. Gao and I. Leader, Sums and k-sums in abelian groups of order k, J. Number Theory 120 (2006), 26-32. [11] W. Gao, Y. Li, J. Peng and F. Sun, Subsums of a zero-sum free subset of an abelian group, Electron J. Combin. 15 (2008), Research Paper 116, 36 pp. [12] A. Geroldinger, Additive group theory and non-unique factorizations, Combinatorial Number Theory and Additive Group Theory, Adv. Course Math. CRM Barcelona, 2009, pp. 1-86. [13] A. Geroldinger and F. Halter-Koch, Non-unique factorizations, Algebraic, Combinatorial and Analytic Theory, Pure Appl. Math. (Boca Raton), 278, 2006. [14] A. Geroldinger and Y. O. Hamidoune, Zero-sumfree sequences in cyclic groups and some arithmetical application, J. Théor. Nombres Bordeaux 14 (2002), 221-239. [15] H. Guan, G. Zeng and P. Yuan, Description of invariant F(5) of a zero-sum free sequence, Acta. Sci. Natur. Univ. Sunyatseni 49 (2010), 1-4 (in Chinese). [16] J. Li and D. Wan, Counting subset sums of finite abelian groups, J. Combin. Theory A 119 (2012), 170-182. [17] M. B. Nathanson, Additive Number Theory: Inverse Problems and the Geometry of Sumsets, Springer Berlin, 1996. [18] J. E. Olson, An addition theorem mod p, J. Combin. Theory 5 (1968), 45-52. [19] J. E. Olson, Sums of sets of group elements, Acta Arith. 28 (1975), 147-156. [20] J. Peng and W. Hui, On the structure of zero-sum free set with minimum subset sums in abelian groups, Ars Combin. 146 (2019), 63-74. [21] P. Yuan and G. Zeng, On zero-sum free subsets of length 7, Electron. J. Combin. 17 (2010), Research Paper 104, 13 pp.
|