A generalization of Meshulam's theorem on subsets of finite abelian groups with no 3-term arithmetic progression (II)
| dc.contributor.author | Liu, Yu-Ru | |
| dc.contributor.author | Spencer, Craig V. | |
| dc.contributor.author | Zhao, Xiaomei | |
| dc.date.accessioned | 2023-10-03T14:55:57Z | |
| dc.date.available | 2023-10-03T14:55:57Z | |
| dc.date.issued | 2011-02 | |
| dc.description | This article is made available through Elsevier's Open Archive, https://doi.org/10.1016/j.ejc.2010.09.008. © 2010 Elsevier Ltd. All rights reserved. | en |
| dc.description.abstract | Let G ≃ Z/k1Z ⊕ · · · ⊕ Z/kN Z be a finite abelian group with ki |ki−1 (2 ≤ i ≤ N). For a matrix Y = (ai,j) ∈ Z R×S satisfying ai,1 + · · · + ai,S = 0 (1 ≤ i ≤ R), let DY (G) denote the maximal cardinality of a set A ⊆ G for which the equations ai,1x1 + · · · + ai,SxS = 0 (1 ≤ i ≤ R) are never satisfied simultaneously by distinct elements x1, . . . , xS ∈ A. Under certain assumptions on Y and G, we prove an upper bound of the form DY (G) ≤ |G|(C/N) γ for positive constants C and γ . | en |
| dc.identifier.uri | https://doi.org/10.1016/j.ejc.2010.09.008 | |
| dc.identifier.uri | http://hdl.handle.net/10012/19989 | |
| dc.language.iso | en | en |
| dc.publisher | Elsevier | en |
| dc.relation.ispartofseries | European Journal of Combinatorics;32(2) | |
| dc.title | A generalization of Meshulam's theorem on subsets of finite abelian groups with no 3-term arithmetic progression (II) | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Liu, Y.-R., Spencer, C. V., & Zhao, X. (2011). A generalization of Meshulam’s theorem on subsets of finite Abelian groups with no 3-term arithmetic progression (II). European Journal of Combinatorics, 32(2), 258–264. https://doi.org/10.1016/j.ejc.2010.09.008 | en |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.contributor.affiliation2 | Pure Mathematics | en |
| uws.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Faculty | en |
| uws.typeOfResource | Text | en |