Siegel's Lemma and Sum-Distinct Sets

2005/03/06 by Iskander Aliev, Aliev, Iskander · 3 citations
Computer Science · Mathematics · #11H06 #11P70 #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0503115

openalex publication_date 2005/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a sharpened form of Siegel Lemma's w. r. t. the maximum norm. This implies a new lower bound on the greatest element of a sum-distinct set of positive integers (Erdös-Moser problem). The main tools are Minkowski's theorem on successive minima and the Busemann theorem from convex geometry.

Cited by

• Central diagonal sections of Gaussian n-cubes
• Combinatorics of slices of cubes
• A Generalisation on Erdős Distinct Subset Sums Problem

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