On zero-sum subsequences in finite Abelian groups.
Schmid, Wolfgang A. (2001)
Integers
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Schmid, Wolfgang A. (2001)
Integers
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Cummings, L.J., Mays, M. (2001)
The Electronic Journal of Combinatorics [electronic only]
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Benjamin Girard (2010)
Colloquium Mathematicae
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We study the minimal number of elements of maximal order occurring in a zero-sumfree sequence over a finite Abelian p-group. For this purpose, and in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian p-groups. Among other consequences, our method implies that, if we denote by exp(G) the exponent of the finite Abelian p-group G considered, every zero-sumfree sequence S with maximal possible...
Canfield, E. Rodney, McKay, Brendan D. (2005)
The Electronic Journal of Combinatorics [electronic only]
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Zhuang, Jujuan (2008)
The Electronic Journal of Combinatorics [electronic only]
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Sergey Avgustinovich, Juhani Karhumäki, Svetlana Puzynina (2012)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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In the paper we study abelian versions of the critical factorization theorem. We investigate both similarities and differences between the abelian powers and the usual powers. The results we obtained show that the constraints for abelian powers implying periodicity should be quite strong, but still natural analogies exist.
Aberkane, Ali, Currie, James D., Rampersad, Narad (2004)
Journal of Integer Sequences [electronic only]
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Carmichael, Richard D., Hayashi, Elmer K. (1981)
International Journal of Mathematics and Mathematical Sciences
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Luise-Charlotte Kappe, M. J. Tomkinson (1998)
Rendiconti del Seminario Matematico della Università di Padova
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Bullock, Evan M. (2004)
The Electronic Journal of Combinatorics [electronic only]
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David B. Penman, Matthew D. Wells (2014)
Acta Arithmetica
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We call a subset A of an abelian group G sum-dominant when |A+A| > |A-A|. If |A⨣A| > |A-A|, where A⨣A comprises the sums of distinct elements of A, we say A is restricted-sum-dominant. In this paper we classify the finite abelian groups according to whether or not they contain sum-dominant sets (respectively restricted-sum-dominant sets). We also consider how much larger the sumset can be than the difference set in this context. Finally, generalising work of Zhao, we provide asymptotic...
Sun, Fang (2007)
The Electronic Journal of Combinatorics [electronic only]
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Szabó, Sándor (2006)
Integers
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