The zero-sum constant, the Davenport constant and their analogues

• Autorzy: Zakarczemny Maciej

Identyfikatory

DOI

10.37705/TechTrans/e2020027

• Języki publikacji: EN

Abstrakty

EN

Let D(G) be the Davenport constant of a finite Abelian group G. For a positive integer m (the case m = 1, is the classical case) let E_m(G) (or η_m(G)) be the least positive integer t such that every sequence of length t in G contains m disjoint zero‑sum sequences, each of length |G| (or of length ≤ exp(G), respectively). In this paper, we prove that if G is an Abelian group, then E_m(G) = D(G) – 1 + m|G|, which generalizes Gao’s relation. Moreover, we examine the asymptotic behaviour of the sequences (E_m(G))_m≥1 and (η_m(G))_m≥1. We prove a generalization of Kemnitz’s conjecture. The paper also contains a result of independent interest, which is a stronger version of a result by Ch. Delorme, O. Ordaz, D. Quiroz. At the end, we apply the Davenport constant to smooth numbers and make a natural conjecture in the non-Abelian case.

Słowa kluczowe

EN

zero-sum sequence; Davenport constant; finite Abelian group

PL

grupa przemienna; grupa abelowa; sekwencja zerowa

• Wydawca: Wydawnictwo Politechniki Krakowskiej im. Tadeusza Kościuszki
• Czasopismo: Technical Transactions
• Rocznik: 2020
• Tom: Vol. 117, iss. 1
• Strony: art. no. e2020027
• Opis fizyczny: Bibliogr. 33 poz., wz.

Twórcy

autor

Zakarczemny Maciej

• Department of Applied Mathematics, Faculty of Computer Science and Telecommunications, Cracow University of Technology

Bibliografia

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Uwagi

Section "Mathematics"

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).