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01/15/2023
Dyck Words, Pattern Avoidance, and Automatic Sequences
We study various aspects of Dyck words appearing in binary sequences, wh...
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09/19/2022
Antisquares and Critical Exponents
The complement x̅ of a binary word x is obtained by changing each 0 in x...
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06/08/2021
On the Average (Edge-)Connectivity of Minimally k-(Edge-)Connected Graphs
Let G be a graph of order n and let u,v be vertices of G. Let κ_G(u,v) d...
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06/17/2020
Extremal overlap-free and extremal β-free binary words
An overlap-free (or β-free) word w over a fixed alphabet Σ is extremal i...
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06/12/2020
The undirected repetition threshold and undirected pattern avoidance
For a rational number r such that 1<r≤ 2, an undirected r-power is a wor...
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02/25/2020
The Threshold Dimension and Irreducible Graphs
Let G be a graph, and let u, v, and w be vertices of G. If the distance ...
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01/31/2020
Lengths of extremal square-free ternary words
A square-free word w over a fixed alphabet Σ is extremal if every word o...
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12/23/2019
The Weak Circular Repetition Threshold Over Large Alphabets
The repetition threshold for words on n letters, denoted (n), is the inf...
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11/13/2019
The Number of Threshold Words on n Letters Grows Exponentially for Every n≥ 27
For every n≥ 27, we show that the number of n/(n-1)^+-free words (i.e., ...
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04/22/2019