Automatic sequences are sequences over a finite alphabet generated by a finite-state
machine. This book presents a novel viewpoint on automatic sequences, and more …

Given a finite alphabet Σ and a right-infinite word w over Σ, we define the Lie complexity
function L w: N→ N, whose value at n is the number of conjugacy classes (under cyclic shift) …

This collaborative volume aims at presenting and developing recent trends at the interface
between the study of sequences, groups, and number theory, as the title may suggest. It is …

For a rational number r such that 1< r≤ 2, an undirected r-power is a word of the form xyx′,
where the word x is nonempty, the word x′ is in {x, x R}, and we have| xyx′|/| xy|= r. The …

We characterize the formulas that are avoided by every $\alpha $-free word for some
$\alpha> 1$. We show that the avoidable formulas whose fragments are of the form $ XY …

In combinatorics on words, a word w over an alphabet\varSigma is said to avoid a pattern p
over an alphabet\varDelta of variables if there is no factor f of w such that f= h (p) where …

We show that, up to renaming of the letters, the only infinite ternary words avoiding the
formula ABCAB. ABCBA. ACB. BAC (resp. ABCA. BCAB. BCB. CBA) have the same set of …

In the interest of studying formulas with reversal of high avoidability index, we find n-
avoidance bases for formulas with reversal for n∈{1, 2, 3}. We demonstrate that there is a …

A family of formulas with reversal of arbitrarily high avoidability index - ScienceDirect Skip to
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We construct an infinite word w over the 5-letter alphabet such that for every factor f of w of
length at least two, there exists a cyclic permutation of f that is not a factor of w. In other …