2023/10/27 by Boris Putievskiy, Putievskiy, Boris
Computer Science · #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2310.18466
openalex publication_date 2023/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article investigates integer sequences that partition the sequence into blocks of various lengths - irregular arrays. The main result of the article is explicit formulas for numbering of irregular arrays. A generalization of Cantor diagonal method is proposed. We also define and describe intra-block permutations of natural numbers. Generalizations of reluctant sequences are introduced, namely generalized reluctant sequences and generalized reverse reluctant sequences. Explicit formulas are presented for these sequences. The article provides numerous examples to illustrate all statements.