## Search

Now showing items 1-10 of 32

#### 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 ...

#### Avoiding approximate repetitions with respect to the longest common subsequence distance

(Mathematical Sciences Publishers, 2015-09-17)

Ochem, Rampersad, and Shallit gave various examples of infinite words avoiding what they called approximate repetitions. An approximate repetition is a factor of the form x x', where x and x' are close to being identical. ...

#### Square-free Words with Square-free Self-shuffles

(The Electronic Journal of Combinatorics, 2014-01-12)

We answer a question of Harju: For every n ≥ 3 there is a square-free ternary word of length n with a square-free self-shuffle.

#### 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 ...

#### 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.

#### 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 ...

#### Multi-dimensional sets recognizable in all abstract numeration systems

(EDP Sciences, 2011)

We prove that the subsets of Nd that are S-recognizable for all abstract numeration systems S are exactly the 1-recognizable sets. This generalizes a result of Lecomte and Rigo in the one-dimensional setting.

#### Cyclically t-complementary uniform hypergraphs

(European Journal of Combinatorics, 2010-05)

A cyclically t-complementary k-hypergraph is a k-uniform hypergraph with vertex set V and edge set E for which there exists a permutation 2 Sym.V/ such that the sets E; E ; E 2; : : : ; E t1 partition the set of all ...

#### On avoidability of formulas with reversal

(EDP Sciences, 2018-02-13)

While a characterization of unavoidable formulas (without reversal) is well-known, little
is known about the avoidability of formulas with reversal in general. In this article, we characterize the unavoidable formulas ...

#### Shuffling and unshuffling

(Bulletin of the European Association for Theoretical Computer Science, 2012)

We consider various shuffling and unshuffling operations on languages and words, and examine their closure properties. Although the main goal is to provide some good and novel exercises and examples for undergraduate formal ...