Weighted EGZ-constant for p-groups of rank 2-Reference-Cited by-同舟云学术

Weighted EGZ-constant for p-groups of rank 2

Published:2019-11 Issue:10 Volume:15 Page:2163-2177
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Oliveira Filipe A. A.¹,Lemos Abílio²,Godinho Hemar T.³

Affiliation:

1. Instituto Federal de Educação, Ciência e Tecnologia, do Rio Grande do Sul-Campus Farroupilha, Farroupilha-RS, Brazil

2. Departamento de Matemática, Universidade Federal de Viçosa, Viçosa-MG, Brazil

3. Departamento de Matemática, Universidade de Brasília, Brasília-DF, Brazil

Abstract

Let [Formula: see text] be a finite abelian group of exponent [Formula: see text], written additively, and let [Formula: see text] be a subset of [Formula: see text]. The constant [Formula: see text] is defined as the smallest integer [Formula: see text] such that any sequence over [Formula: see text] of length at least [Formula: see text] has an [Formula: see text]-weighted zero-sum subsequence of length [Formula: see text] and [Formula: see text] defined as the smallest integer [Formula: see text] such that any sequence over [Formula: see text] of length at least [Formula: see text] has an [Formula: see text]-weighted zero-sum subsequence of length at most [Formula: see text]. Here, we prove that, for [Formula: see text], and [Formula: see text], we have [Formula: see text] and classify all the extremal [Formula: see text]-weighted zero-sum free sequences.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042119501197

Reference15 articles.

1. Zero-sum problems with subgroup weights

2. Some zero-sum constants with weights

3. Contributions to zero-sum problems

4. On weighted zero-sum sequences

5. New upper bounds for the Davenport and for the Erdős–Ginzburg–Ziv constants

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1. Weighted zero-sum constants for $$\varvec{p}$$-groups;Proceedings - Mathematical Sciences;2024-02-15

2. On monoids of weighted zero-sum sequences and applications to norm monoids in Galois number fields and binary quadratic forms;Acta Mathematica Hungarica;2022-10

3. A weighted Erdős–Ginzburg–Ziv constant for finite abelian groups with higher rank;Proceedings - Mathematical Sciences;2022-03-22