Representation of group elements as subsequence sums
نویسندگان
چکیده
منابع مشابه
Representation of Finite Abelian Group Elements by Subsequence Sums
Let G ∼= Cn1 ⊕ · · · ⊕ Cnr be a finite and nontrivial abelian group with n1|n2| . . . |nr. A conjecture of Hamidoune says that if W = w1 · · ·wn is a sequence of integers, all but at most one relatively prime to |G|, and S is a sequence over G with |S| ≥ |W |+ |G| − 1 ≥ |G| + 1, the maximum multiplicity of S at most |W |, and σ(W ) ≡ 0 mod |G|, then there exists a nontrivial subgroup H such tha...
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We prove that every group G of order n has t,log n/log 2+0dog log n) elements x, x, such that every group element is a product of the form x,'-• X,'% e ; s 1,0, 11. The result is true more generally for quasigroups. As a corollary we obtain that for n even, every one-factorization of the complete graph on n vertices contains at most r one-factors whose union is connected. The aim of this note i...
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Let G be an abelian group, let S be a sequence of terms s1, s2, . . . , sn ∈ G not all contained in a coset of a proper subgroup of G, and let W be a sequence of n consecutive integers. Let W ̄ S = {w1s1 + . . . + wnsn : wi a term of W, wi 6= wj for i 6= j}, which is a particular kind of weighted restricted sumset. We show that |W ̄S| ≥ min{|G| − 1, n}, that W ̄ S = G if n ≥ |G| + 1, and also c...
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provided an = sin (wn/2) and k(x) =sin (irx/2). Weinberger [8] treated the case when the coefficients a„ form a periodic sequence; that is an+q = a„ for some integer q. Making use of the character theory of Dirichlet 7-functions, he found the conditions on the a„ so that (3) holds with the kernel (2/q112) cos (2irx/q) or the kernel (2/q112) sin (2irx/q). (These kernels give self-reciprocal tran...
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Here sn x is an abbreviation for sin (wx/2). This paper gives other conditions for the validity of these identities. The previous conditions permitted to have various types of discontinuity. The present paper is concerned with smooth functions; however, the growth at 0 and «> is permitted to be greater than before. Theorems 1, 2, and 3 of the previous paper together with Theorems 2 and 3 of...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.06.037