2017/02/08 by Enrique Navarrete, Navarrete, Enrique
Computer Science · Mathematics · #Cellular Automata and Applications #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #math.CO #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1702.02637
arxiv created 2017/02/08 · openalex publication_date 2017/02/08 · arxiv updated 2017/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we define circular k-successions in permutations in one-line notation and count permutations that avoid substrings j(j+k) and j(j+k) (mod n). We also count circular permutations that avoid such substrings, and show that for substrings j(j+k) (mod n), the number of permutations depends on whether n is prime, and more generally, on whether n and k are relatively prime.