2020/07/19 by Tanya Khovanova, Kevin C.‐W. Wu, Khovanova, Tanya +1
Computer Science · Engineering · #11B25 #Computability, Logic, AI Algorithms #FOS: Mathematics #Number Theory (math.NT) #graph theory and CDMA systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2007.09705
openalex publication_date 2020/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We delve into the connection between base (3)/(2) and the greedy partition of non-negative integers into 3-free sequences. Specifically, we find a fractal structure on strings written with digits 0, 1, and 2. We use this structure to prove that the even non-negative integers written in base (3)/(2) and then interpreted in base 3 form the Stanley cross-sequence, where the Stanley cross-sequence comprises the first terms of the infinitely many sequences that are formed by the greedy partition of non-negative integers into 3-free sequences.