2017/03/08 by Rob Burns, Burns, Rob
Computer Science · #11B65 #Cellular Automata and Applications #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1703.02705
openalex publication_date 2017/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Cn be the nth Catalan number. For any prime p ≥ 5 we show that the set \Cn : n ∈ ℕ \ contains all residues mod p. In addition all residues are attained infinitely often. Any positive integer can be expressed as the product of central binomial coefficients modulo p. The directed sub-graph of the automata for Cn \mod p consisting of the constant states and transitions between them has a cycle which visits all vertices.