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math.DS2013
On digit frequencies in β-expansions
Philip Boyland, André de Carvalho, Toby Hall
We study the sets DF(β) of digit frequencies of β-expansions of numbers in [0,1]. We show that DF(β) is a compact convex set with countably many extreme points which varies continu…
math.DS2013★ 4 cited
Symbol ratio minimax sequences in the lexicographic order
Philip Boyland, André de Carvalho, Toby Hall
Consider the space of sequences of k letters ordered lexicographically. We study the set M(α) of all maximal sequences for which the asymptotic proportions α of the letters are pre…