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Zero-sum problems in finite abelian groups: A survey
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“Theorem 1.1 If G is a finite abelian group of order n , then E ( G ) = D ( G )+ n -1 .”
From Davenport constant with weights (2010) · cites this paper as [7]
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Cites
Alon, N. (1999) · Combinatorics Probability Computing · doi:10.1017/s0963548398003411 · Cited by 653
Lang, S. (1991) · Encyclopaedia of mathematical sciences · doi:10.1007/978-3-642-58227-1 · Cited by 513
Additive number theory: inverse problems and the geometry of sumsets
(1997) · Choice Reviews Online · doi:10.5860/choice.35-0343a · Cited by 414
Non-Unique Factorizations: Algebraic, Combinatorial and Analytic Theory
Geroldinger, A., & Halter-Koch, F. (2006) · doi:10.1201/9781420003208 · Cited by 366
Self-citationHooley, C. (1967) · Journal für die reine und angewandte Mathematik (Crelles Journal) · doi:10.1515/crll.1967.225.209 · Cited by 353
Foundations of a Structural Theory of Set Addition
Freiman, G. (2007) · Translations of Mathematical Monographs · doi:10.1090/mmono/037 · Cited by 347
There are Infinitely Many Carmichael Numbers
Alford, W. R., Granville, A., & Pomerance, C. (1994) · The Annals of Mathematics · doi:10.2307/2118576 · Cited by 333
A combinatorial problem on finite Abelian groups, I
Olson, J. E. (1969) · Journal of Number Theory · doi:10.1016/0022-314x(69)90021-3 · Cited by 290
Cyclic Spaces for Grassmann Derivatives and Additive Theory
da Silva, J. A. D., & Hamidoune, Y. O. (1994) · Bulletin of the London Mathematical Society · doi:10.1112/blms/26.2.140 · Cited by 174
Motwani, R., & Raghavan, P. (1995) · Cambridge University Press eBooks · doi:10.1017/cbo9780511814075.015 · Cited by 148
Research works printed but not linked: 19
- Bialostocki, 2000, Zero-sum ascending waves, J. Combin. Math. Combin. Comput., 32, 103
- Bialostocki, 1990, Zero sum Ramsey theorems, Congr. Numer., 70, 119
- A. Bialostocki, M. Lotspeich, Some developments of the Erdős–Ginzburg–Ziv theorem, in: Sets, Graphs and Numbers, vol. 60, Colloquia Mathematica Societatis Janos Bolyai, North-Holland, Amsterdam, New York, 1992, pp. 97–117.
- Chapman, 2002, On Davenport's constant of finite abelian groups, Far East J. Math. Sci., 2, 47
- Chiaselotti, 1993, Sums of distinct elements in finite abelian groups, Boll. Unione Mat. Ital., 7, 243
- Dimitrov, 2004, On the strong Davenport constant of nonabelian finite p-groups, Math. Balkica, 18, 131
- Erdős, 1961, Theorem in the additive number theory, Bull. Res. Council Israel, 10, 41
- M. Freeze, Lengths of factorizations in Dedekind domains, Ph.D. Thesis, University of North Carolina at Chapel Hill, 1999.
- Freeze, 2001, Sumsets of zerofree sequences, Arab J. Sci. Eng. Section C: Theme Issues, 26, 97
- Z. Füredi, D.J. Kleitman, The minimal number of zero sums. in: Combinatorics, Paul Erdős is Eighty, J. Bolyai Mathematical Society, 1993, pp. 159–172.
- Gallardo, 2000, On Brakemeier's variant of the Erdős–Ginzburg–Ziv problem, Tatra Mt. Math. Publ., 20, 91
- W. Gao, Some problems in additive group theory and number theory, Ph.D. Thesis, Sichuan University, Sichuan, PR China, 1994.
- Gao, 1996, An improvement of Erdős–Ginzburg–Ziv theorem, Acta Math. Sin., 39, 514
- Kemnitz, 1983, On a lattice point problem, Ars. Combin., 16-B, 151
- Krause, 1991, Arithmetic in Krull monoids and the cross number of divisor class groups, Mitt. Math. Ges. Hamb., 12, 681
- E. Lipkin, Subset sums of sets of residues. in: Structure Theory of Set Addition, vol. 258, Astérisque, 1999, pp. 187–192.
- Ordaz, 2006, On zero-free sets, Divulg. Mat., 14, 1
- Schmid, 2005, Half-factorial sets in finite abelian groups: a survey, Grazer Math. Ber., 348, 41
- Skałba, 1992, The relative Davenport's constant of the group Zn×Zn, Grazer Math. Ber., 318, 167
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Metadata
- Authors
- Gao, W., & Geroldinger, A.
- Affiliations
- Nankai University (CN)
- University of Graz (AT)
- Corresponding author
- Geroldinger, Alfred
- Venue
- Expositiones Mathematicae
- Publisher
- Elsevier BV
- Published
- 2006-11
- Volume
- 24
- Issue
- 4
- Pages
- 337-369
- ISSN
- 0723-0869 (ISSN-L)
- OpenAlex
- W2121001629
- Cited by
- 262
- References
- 152
- Citations by year
- 2026: 19 · 2025: 13 · 2024: 13 · 2023: 11 · 2022: 15 · 2021: 15 · 2020: 18 · 2019: 14 · 2018: 11 · 2017: 10 · 2016: 3 · 2015: 13 · 2014: 13 · 2013: 13 · 2012: 11
- FWCI
- 17.93
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.elsevier.com/tdm/userlicense/1.0/ (tdm)
- www.elsevier.com/open-access/userlicense/1.0/ (vor, 2452 d)
- Locations
- Expositiones Mathematicae (publishedVersion)
- Funders
- National Natural Science Foundation of China
- Austrian Science Fund
- Topics
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Advanced Combinatorial Mathematics
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Limits and Structures in Graph Theory
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Finite Group Theory Research
- Keywords
- zero-sum problems, finite abelian groups, combinatorial number theory, Davenport constant, algebraic invariants
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