Modified Erdős-Ginzburg-Ziv Constants for (ℤ/nℤ)²

2019/07/25 by Hammonds, Trajan
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.11236

Abstract

For an abelian group G and an integer t > 0, the modified Erdős-Ginzburg-Ziv constant s'_t(G) is the smallest integer ℓ such that any zero-sum sequence of length at least ℓ with elements in G contains a zero-sum subsequence (not necessarily consecutive) of length t. We compute bounds for s'_t(G) for G = (ℤ/nℤ)² and G = (ℤ/n₁ℤ × ℤ/n₂ℤ). We also compute bounds for G = (ℤ/pℤ)^d where the subsequence can be any length in \p, …, (d-1)p\. Lastly, we investigate the Erdős-Ginzburg-Ziv constant for G = (ℤ/nℤ)² and subsequences of length tn.

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