Article
The H-Critical Number of Finite Abelian Groups
Authors
Abstract
For a finite abelian group G and a positive integer h, the unre- stricted (resp. restricted) h-critical number χ(G, h) (resp. χˆ(G, h)) of G is defined to be the minimum value of m, if exists, for which the h-fold unrestricted (resp. re- stricted) sumset of every m-subset of G equals G itself. Here we determine χ(G, h) for all G and h; and prove several results for χˆ(G, h), including the cases of any G and h = 2, any G and large h, and any h for the cyclic group Z n of even order. We also provide a lower bound for χˆ(Z n, 3) that we believe is exact for every n—this conjecture is a generalization of the one made by Gallardo, Grekos, et al. that was proved (for large n) by Lev.
Keywords
critical number, abelian groups, sumsets, restricted sumsets.
Citation
Bajnok, B. (2015). The h-critical number of finite abelian groups. Uniform Distribution Theory, 10(2), 93–115.
B. Bajnok, “The h-critical number of finite abelian groups,” Uniform Distribution Theory, vol. 10, no. 2, pp. 93–115, 2015.
Bajnok B. The h-critical number of finite abelian groups. Uniform Distribution Theory. 2015;10(2):93–115.
Bajnok, B. (2015), ‘The h-critical number of finite abelian groups’, Uniform Distribution Theory, 10(2), pp. 93–115.
Bajnok, Bela. “The H-critical Number of Finite Abelian Groups.” Uniform Distribution Theory, vol. 10, no. 2, 2015, pp. 93–115.
Bajnok, Bela. “The H-critical Number of Finite Abelian Groups.” Uniform Distribution Theory 10, no. 2 (2015): 93–115.
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Published by: Engineering Journals
