Article
Weighted Sums in Finite Abelian Groups
Authors
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Abstract
In this note we prove the following weighted generalization of Bollob´as and Leader theorem (J. Number Theory 78 (1999), no. 1, 27–35): Let G be an abelian group of order n and k a positive integer. Let (w1, w2, . . . , w k ) be a sequence of integers where each wi is co-prime to n. Then, given a sequence (x1, x2, . . . , x k+r ) of elements of G,where 1 ≤ r ≤ n − 1, if 0 is the most re- peated element in the sequence, and k 1 wix σ(i) =0, for all permutations σ of {1, 2, . . . , k + r}, we havekwix σ(i) : σ is a permutation of {1, 2, . . . , k + r}≥ r + 1.
Keywords
Abelian group, permutation, weighted sum.
Citation
Adhikari, S., Chintamani, M., Moriya, B., & Paul, P. (2008). Weighted sums in finite abelian groups. Uniform Distribution Theory, 3(1), 105–110.
S. Adhikari, M. Chintamani, B. Moriya and P. Paul, “Weighted sums in finite abelian groups,” Uniform Distribution Theory, vol. 3, no. 1, pp. 105–110, 2008.
Adhikari S, Chintamani M, Moriya B, Paul P. Weighted sums in finite abelian groups. Uniform Distribution Theory. 2008;3(1):105–110.
Adhikari, S., Chintamani, M., Moriya, B. and Paul, P. (2008), ‘Weighted sums in finite abelian groups’, Uniform Distribution Theory, 3(1), pp. 105–110.
Adhikari, S.d., et al. “Weighted Sums in Finite Abelian Groups.” Uniform Distribution Theory, vol. 3, no. 1, 2008, pp. 105–110.
Adhikari, S.d., M.n. Chintamani, B.k. Moriya, and P. Paul. “Weighted Sums in Finite Abelian Groups.” Uniform Distribution Theory 3, no. 1 (2008): 105–110.
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Published by: Engineering Journals
