Combinatorial properties of lazy expansions in Cantor real bases

2022/02/01 by Cisternino, Célia
#11A63 #11K16 #37B10 #68Q45 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.2202.00437

Abstract

The lazy algorithm for a real base β is generalized to the setting of Cantor bases \boldsymbolβ=(β_n)_{n∈ ℕ} introduced recently by Charlier and the author. To do so, let x_{\boldsymbolβ} be the greatest real number that has a \boldsymbolβ-representation a₀a₁a₂⋯ such that each letter a_n belongs to \0,…,\lceil β_n \rceil -1\. This paper is concerned with the combinatorial properties of the lazy \boldsymbolβ-expansions, which are defined when x_{\boldsymbolβ}

Related

• Expansions in Cantor real bases
• Computing Expansions in Infinitely Many Cantor Real Bases via a Single Transducer
• Dynamical behavior of alternate base expansions
• Expansions of real numbers in non-integer bases and charaterisation of Lazy expansion of 1
• An analogue of Solomyak's theorem for periodic Cantor real expansions in alternate bases