2022/12/23 by Jason P. Bell, Jeffrey Shallit, Bell, Jason P. +1
Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2212.12473
openalex publication_date 2022/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We disprove a 2002 conjecture of Dombi from additive number theory. More precisely, we find examples of sets A ⊂ ℕ with the property that ℕ ∖ A is infinite, but the sequence n → |\ (a,b,c) : n=a+b+c and a,b,c ∈ A \|, counting the number of 3-compositions using elements of A only, is strictly increasing.