When is an automatic set an additive basis?

2017/10/23 by Jason Bell, Bell, Jason, Kathryn Hare +3 · 1 citation
Computer Science · Mathematics · #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Number Theory (math.NT) #cs.DM #cs.FL #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.1710.08353

arxiv created 2017/10/23 · arxiv updated 2017/10/24

Abstract

We characterize those k-automatic sets S of natural numbers that form an additive basis for the natural numbers, and we show that this characterization is effective. In addition, we give an algorithm to determine the smallest j such that S forms an additive basis of order j, if it exists.

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