2013/05/06 by J. A. Dias da Silva, da Silva, J. A. Dias, Pedro J. Freitas +1
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #Matrix Theory and Algorithms #math.CO
paper · pdf · doi:10.48550/arxiv.1305.1139
arxiv created 2013/05/06 · openalex publication_date 2013/05/06 · arxiv updated 2013/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The sum-product conjecture of Erd\H os and Szemerédi states that, given a finite set A of positive numbers, one can find asymptotic lower bounds for max\|A+A|,|A⋅ A|\ of the order of |A|1+δ for every δ<1. In this paper we consider the set of all spectral radii of n× n matrices with entries in A, and find lower bounds for the cardinality of this set. In the case n=2, this cardinality is necessarily larger than max\|A+A|,|A⋅ A|\.