The Davenport constant of a box

• Autorzy: Alain Plagne
• Języki publikacji: EN

Abstrakty

EN

Given an additively written abelian group G and a set X ⊆ G, we let 𝓑(X) denote the monoid of zero-sum sequences over X and 𝖣(X) the Davenport constant of 𝓑(X), namely the supremum of the positive integers n for which there exists a sequence x₁⋯xₙ in 𝓑(X) such that $∑_{i ∈ I} x_i ≠ 0$ for each non-empty proper subset I of {1,...,n}. In this paper, we mainly investigate the case when G is a power of ℤ and X is a box (i.e., a product of intervals of G). Some mixed sets (e.g., the product of a group by a box) are studied too, and some inverse results are obtained.

Kategorie tematyczne

• 11B75: Other combinatorial number theory
• 11P70: Inverse problems of additive number theory, including sumsets
• 11B30: Arithmetic combinatorics; higher degree uniformity

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 171
• Numer: 3
• Strony: 197-219

Daty

wydano

2015

Twórcy

autor

Alain Plagne

• Centre de mathématiques Laurent Schwartz, École polytechnique, 91128 Palaiseau Cedex, France

Identyfikatory

DOI

10.4064/aa171-3-1