A generalization of Meshulam's theorem on subsets of finite abelian groups with no 3-term arithmetic progression
| dc.contributor.author | Liu, Yu-Ru | |
| dc.contributor.author | Spencer, Craig V. | |
| dc.date.accessioned | 2023-10-03T15:10:47Z | |
| dc.date.available | 2023-10-03T15:10:47Z | |
| dc.date.issued | 2009-01-31 | |
| dc.description | This is a post-peer-review, pre-copyedit version of an article published in Designs, Codes and Cryptography. The final authenticated version is available online at: https://doi.org/10.1007/s10623-009-9268-0 | en |
| dc.description.abstract | Let r1, . . . , rs be non-zero integers satisfying r1 + · · · + rs = 0. Let G Z/k1Z⊕· · ·⊕Z/knZ be a finite abelian group with ki |ki−1(2 ≤ i ≤ n), and suppose that (ri , k1) = 1(1 ≤ i ≤ s). Let Dr(G) denote the maximal cardinality of a set A ⊆ G which contains no non-trivial solution of r1x1+· · · +rs xs = 0 with xi ∈ A(1 ≤ i ≤ s).We prove that Dr(G) |G|/ns−2. We also apply this result to study problems in finite projective spaces. | en |
| dc.identifier.uri | https://doi.org/10.1007/s10623-009-9268-0 | |
| dc.identifier.uri | http://hdl.handle.net/10012/19999 | |
| dc.language.iso | en | en |
| dc.publisher | Springer | en |
| dc.relation.ispartofseries | Designs, Codes and Cryptography;52 | |
| dc.subject | Roth's theorem | en |
| dc.subject | finite abelian groups | en |
| dc.subject | character sums | en |
| dc.title | A generalization of Meshulam's theorem on subsets of finite abelian groups with no 3-term arithmetic progression | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Liu, Y.-R., & Spencer, C. V. (2009). A generalization of Meshulam’s theorem on subsets of finite Abelian groups with no 3-term arithmetic progression. Designs, Codes and Cryptography, 52(1), 83–91. https://doi.org/10.1007/s10623-009-9268-0 | 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 |