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  • A generalization of Kneser's Addition Theorem [Elektronski vir]
    DeVos, Matt ; Goddyn, Luis ; Mohar, Bojan, 1956-
    Let ▫$A = (A_1,\ldots,A_m)$▫ be a sequence of finite subsets from an additive abelian group ▫$G$▫. Let ▫$\Sigma^{\ell}(A)$▫ denote the set of all group elements representable as a sum of ▫$\ell$▫ ... elements from distinct terms of ▫$A$▫, and set ▫$H = $▫stab▫$(\Sigma^{\ell}(A)) = \{ g \in G : g + \Sigma^{\ell}(A) = \Sigma^{\ell}(A) \}$▫. Our main theorem is the following lower bound: ▫$$|\Sigma^{\ell}(A)| \ge |H| \Bigl(1 - \ell + \sum_{Q \in G/H} \min \bigl\{ \ell, \#\{i \in \{1,\ldots,m\} : A_i \cap Q \neq \emptyset \} \bigr\} \Bigr).$$▫ In the special case when ▫$m=\ell=2$▫, this is equivalent to Kneser's addition theorem, and indeed we obtain a new proof of this result. The special case when every ▫$A_i$▫ has size one is a new result concerning subsequence sums which extends some recent work of Bollobás-Leader, Hamidoune, Hamidoune-Ordaz-Ortuño, Grynkiewicz, and Gao, and resolves two recent conjectures of Gao, Thangadurai, and Zhuang.
    Vir: Preprint series. - ISSN 1318-4865 (Vol. 45, št. 1032, 2007, str. 1-23)
    Vrsta gradiva - e-članek
    Leto - 2007
    Jezik - angleški
    COBISS.SI-ID - 14784345

    Povezava(-e):

    http://www.imfm.si/preprinti/PDF/01032.pdf

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