
When is an automatic set an additive basis?
We characterize those kautomatic sets S of natural numbers that form an...
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Natural exact covering systems and the reversion of the Möbius series
We prove that the number of natural exact covering systems of cardinalit...
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Waring's Theorem for Binary Powers
A natural number is a binary k'th power if its binary representation con...
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Subword complexity and power avoidance
We begin a systematic study of the relations between subword complexity ...
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Lengths of Words Accepted by Nondeterministic Finite Automata
We consider two natural problems about nondeterministic finite automata....
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Rollercoasters and Caterpillars
A rollercoaster is a sequence of real numbers for which every maximal co...
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Circular critical exponents for ThueMorse factors
We prove various results about the largest exponent of a repetition in a...
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Critical exponent of infinite balanced words via the Pell number system
In a recent paper of Rampersad et al., the authors conjectured that the ...
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Generalized de Bruijn words and the state complexity of conjugate sets
We consider a certain natural generalization of de Bruijn words, and use...
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Circularly squarefree words and unbordered conjugates: a new approach
Using a new approach based on automatic sequences, logic, and a decision...
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New results on pseudosquare avoidance
We start by considering binary words containing the minimum possible num...
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Borders, Palindrome Prefixes, and Square Prefixes
We show that the number of lengthn words over a kletter alphabet havin...
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Words With Few Palindromes, Revisited
In 2013, Fici and Zamboni proved a number of theorems about finite and i...
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Words Avoiding Reversed Factors, Revisited
In 2005, Rampersad and the second author proved a number of theorems abo...
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Avoidance of split overlaps
We generalize Axel Thue's familiar definition of overlaps in words, and ...
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New Bounds on Antipowers in Binary Words
Fici et al. defined a word to be a kpower if it is the concatenation of...
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Computational Aspects of Sturdy and Flimsy Numbers
Following Stolarsky, we say that a natural number n is flimsy in base b ...
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An inequality for the number of periods in a word
We prove an inequality for the number of periods in a word x in terms of...
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Extremal overlapfree and extremal βfree binary words
An overlapfree (or βfree) word w over a fixed alphabet Σ is extremal i...
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Sumsets of Wythoff Sequences, Fibonacci Representation, and Beyond
Let α = (1+√(5))/2 and define the lower and upper Wythoff sequences by a...
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A Frameless 2Coloring of the Plane Lattice
A picture frame in two dimensions is a rectangular array of symbols, wit...
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Decidability and kRegular Sequences
In this paper we consider a number of natural decision problems involvin...
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Jeffrey Shallit
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