Szczegóły publikacji
Opis bibliograficzny
Partition of Abelian groups into zero-sum sets by complete mappings and its application to the existence of a magic rectangle set / Sylwia CICHACZ // Journal of Algebraic Combinatorics ; ISSN 0925-9899. — 2025 — vol. 61 iss. 2 art. no. 24, s. 1-11. — Bibliogr. s. 11, Abstr. — Publikacja dostępna online od: 2025-02-26
Autor
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 158409 |
|---|---|
| Data dodania do BaDAP | 2025-03-29 |
| Tekst źródłowy | URL |
| DOI | 10.1007/s10801-025-01392-9 |
| Rok publikacji | 2025 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Journal of Algebraic Combinatorics |
Abstract
A complete mapping of a group is a bijection for which the mapping is a bijection. In this paper we consider the existence of a complete mapping of an Abelian group and a partition of elements of such that for every i, . A -magic rectangle set of order abc is a collection of c arrays whose entries are elements of an Abelian group of order abc, each appearing once, with all row sums in every rectangle equal to the constant and all column sums in every rectangle equal to the constant . While a complete characterization of exists for cases where , the scenario where remains unsolved for . Using the partition of into zero-sum sets by complete mappings, we give some sufficient conditions that a -magic rectangle set exists.
