Abstract
For an abelian group G, the Davenport constant D(G) is defined to be the smallest natural number k such that any sequence of k elements in G has a nonempty subsequence whose sum is zero (the identity element). Motivated by some recent developments around the notion of Davenport constant with weights, we study them in some basic cases. We also define a new combinatorial invariant related to (ℤ/nℤ)d, more in the spirit of some constants considered by Harborth and others and obtain its exact value in the case of (ℤ/nℤ)2 where n is an odd integer.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adhikari S D, Chen Y G, Friedlander J B, Konyagin S V and Pappalardi F, Contributions to zero-sum problems, Discrete Math. 306 (2006) 1–10
Adhikari S D and Chen Y G, Davenport constant with weights and some related questions —II, J. Combin. Theory A115 (2008) 178–184
Adhikari Sukumar Das and Rath Purusottam, Davenport constant with weights and some related questions, Integers 6 (2006) paper A 30
Alon N and Dubiner M, A lattice point problem and additive number theory, Combinatorica 15 (1995) 301–309
Cauchy A L, Recherches sur les nombres, J. Ecôle Polytech. 9 (1813) 99–123
Davenport H, On the addition of residue classes, J. London Math. Soc. 22 (1947) 100–101
Elsholtz Christian, Lower bounds for multidimensional zero sums, Combinatorica 24(3) (2004) 351–358
Florian Luca, A generalization of a classical zero-sum problem, Discrete Math. 307(13) (2007) 1672–1678
Harborth H, Ein Extremalproblem für Gitterpunkte, J. Reine Angew. Math. 262/263 (1973) 356–360
Kemnitz A, On a lattice point problem, Ars Combin. 16b (1983) 151–160
Nathanson Melvyn B, Additive Number Theory: Inverse Problems and the Geometry of Sumsets (Springer) (1996)
Reiher Christian, On Kemnitz’s conjecture concerning lattice points in the plane, Ramanujan J. 13(1–3) (2007) 333–337
Rónyai L, On a conjecture of Kemnitz, Combinatorica 20(4) (2000) 569–573
Serre J-P, A course in arithmetic (Springer) (1973)
Thangadurai R, A variant of Davenport’s constant, Proc. Indian Acad. Sci. (Math. Sci.) 117(2) (2007) 147–158
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Adhikari, S.D., Balasubramanian, R., Pappalardi, F. et al. Some zero-sum constants with weights. Proc Math Sci 118, 183–188 (2008). https://doi.org/10.1007/s12044-008-0010-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12044-008-0010-z