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Displaying 241 – 260 of 281

Sums of the form $1 / x_{1}^{k} + \dots + 1 / x_{n}^{k}$ modulo a prime.

Croot, Ernie (2004)

Integers

Sumsets avoiding squarefree integers

Jan-Christoph Schlage-Puchta (2010)

Acta Arithmetica

Sumsets in quadratic residues

I. D. Shkredov (2014)

Acta Arithmetica

We describe all sets $A \subseteq_{p}$ which represent the quadratic residues $R \subseteq_{p}$ in the sense that R = A + A or R = A ⨣ A. Also, we consider the case of an approximate equality R ≈ A + A and R ≈ A ⨣ A and prove that A is then close to a perfect difference set.

Sumsets of finite Beatty sequences.

Pitman, Jane (2001)

The Electronic Journal of Combinatorics [electronic only]

Sure monochromatic subset sums

Noga Alon, Paul Erdős (1996)

Acta Arithmetica

Symmetric subsets of lattice paths.

Verbitsky, Oleg (2000)

Integers

Tableau cycling and Catalan numbers.

Buontempo, Jenny, Hopkins, Brian (2007)

Integers

The class of Erdős-Turán sets

G. Grekos, L. Haddad, C. Helou, J. Pihko (2005)

Acta Arithmetica

The Coefficients of Cosh x/cos x.

L. Carlitz (1965)

Monatshefte für Mathematik

The Davenport constant of a box

Alain Plagne (2015)

Acta Arithmetica

Given an additively written abelian group G and a set X ⊆ G, we let (X) denote the monoid of zero-sum sequences over X and (X) the Davenport constant of (X), namely the supremum of the positive integers n for which there exists a sequence x₁⋯xₙ in (X) such that $\sum_{i \in I} x_{i} \neq 0$ 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...