Szczegóły publikacji
Opis bibliograficzny
Disjoint zero-sum subsets in Abelian groups and their application: a survey / Sylwia CICHACZ // W: Sum(m)it280 : surveys in extremal combinatorics and combinatorial geometry / eds. Gyula O. H. Katona, Balázs Patkós, Casey Tompkins. — Cham : Springer, cop. 2026. — ( Bolyai Society Mathematical Studies ; ISSN 1217-4696 ; vol. 32 ). — ISBN: 978-3-032-18809-0; e-ISBN: 978-3-032-18810-6. — S. 133–145. — Bibliogr., Abstr. — Publikacja dostępna online od: 2026-05-28
Autor
Dane bibliometryczne
| ID BaDAP | 168243 |
|---|---|
| Data dodania do BaDAP | 2026-07-08 |
| DOI | 10.1007/978-3-032-18810-6_6 |
| Rok publikacji | 2026 |
| Typ publikacji | fragment książki |
| Otwarty dostęp |  |
| Wydawca | Springer |
| Czasopismo/seria | Bolyai Society Mathematical Studies |
Abstract
We provide a summary of research on disjoint zero-sum subsets in finite Abelian groups, which is a branch of additive group theory and combinatorial number theory. An orthomorphism of a group Γ is defined as a bijection φ of Γ such that the mapping g↦g-1φ(g) is also bijective. In 1981, Friedlander, Gordon, and Tannenbaum conjectured that when Γ is Abelian, for any k≥2 dividing |Γ|-1, there exists an orthomorphism of Γ fixing the identity and permuting the remaining elements as products of disjoint k-cycles. Using the idea of disjoint zero-sum subsets, we provide a solution of this conjecture for k=3 and |Γ|≡4(mod24). We also present some applications of zero-sum sets in graph labeling.
