## Search

Now showing items 1-10 of 39

#### Avoidability index for binary patterns with reversal

(2017)

For every pattern p over the alphabet {x,x^R,y,y^R}, we specify the least k such that p is k-avoidable.

#### A direct proof of a result of Thue

(Utilitas Mathematica, 1984)

#### Avoiding Patterns in the Abelian Sense

(Canadian Mathematical Society, 2001-08)

We classify all 3 letter patterns that are avoidable in the abelian sense. A short list of four letter patterns for which abelian avoidance is undecided is given. Using a generalization of Zimin words we deduce some ...

#### For each a > 2 there is an Infinite Binary Word with Critical Exponent a

(The Electronic Journal of Combinatorics, 2008-08-31)

The critical exponent of an infinite word w is the supremum of all rational numbers α such that w contains an α-power. We resolve an open question of Krieger and Shallit by showing that for each α>2 there is an infinite ...

#### A family of formulas with reversal of high avoidability index

(World Scientific, 2017)

We present an infinite family of formulas with reversal whose avoidability index is bounded between 4 and 5, and we show that several members of the family have avoidability index 5. This family is particularly interesting ...

#### Abelian complexity of fixed point of morphism 0 ↦ 012, 1 ↦ 02, 2 ↦ 1

(Integers, 2014-02-20)

We study the combinatorics of vtm, a variant of the Thue-Morse word generated by the non-uniform morphism 0 ↦ 012, 1 ↦ 02, 2 ↦ 1 starting with 0. This infinite ternary sequence appears a lot in the literature and finds ...

#### Attainable lengths for circular binary words avoiding k-powers

(The Belgian Mathematical Society, 2005)

We show that binary circular words of length n avoiding 7/3+ powers exist
for every sufficiently large n. This is not the case for binary circular words
avoiding k+ powers with k < 7/3

#### The Brachistochrone Problem: Mathematics for a Broad Audience via a Large Context Problem

(Montana Council of Teachers of Mathematics & Information Age Publishing, 2008)

Large context problems (LCP) are useful in teaching the history of science. In this article we consider the brachistochrone problem in a context stretching from Euclid through the Bernoullis. We highlight a variety of ...

#### Extremal words in morphic subshifts

(Elsevier, 2014-01-22)

Given an infinite word x over an alphabet A, a letter b occurring in
x, and a total order \sigma on A, we call the smallest word with respect to \sigma
starting with b in the shift orbit closure of x an extremal word of ...

#### Unary patterns under permutations

(Elsevier, 2018-06-04)

Thue characterized completely the avoidability of unary patterns. Adding function variables gives a general setting capturing avoidance of powers, avoidance of patterns with palindromes, avoidance of powers under coding, ...