## 12 Citations

### On p-adic avoidance of words

- Mathematics
- 2009

In this paper a new modification of the notion of avoidance of words is introduced. We say, that a word w p-adically avoids a word u, if u does not belong to the set of all words whose symbols occur…

### Some further results on squarefree arithmetic progressions in infinite words

- MathematicsTheor. Comput. Sci.
- 2019

### On some problems of Harju concerning squarefree arithmetic progressions in infinite words

- Mathematics
- 2018

In a recent paper, Harju posed three open problems concerning square-free arithmetic progressions in infinite words. In this note we solve two of them.

### Repetitions in Toeplitz Words and the Thue Threshold

- MathematicsCiE
- 2020

It is shown that the Toeplitz word generated by any sequence of primitive partial words of maximal length k is k-th power-free, and the existence of a 2-colouring of the integer lattice points in the Euclidean plane such that the sequence of colours of consecutive points on any straight line does not contain squares of length larger than 26.

### A Narad Rampersad

- Mathematics
- 2007

U. Schmidt proved that any binary pattern of length at least 1 3 is avoided by either the Thue–Morse word or the Fibonacci word. We give a somewhat simpler proof of this result.

### Avoiding Multiple Repetitions in Euclidean Spaces

- MathematicsSIAM J. Discret. Math.
- 2020

We study colorings of Euclidean spaces avoiding specified patterns on straight lines. This extends the seminal work of Thue on avoidability properties of sequences to continuous, higher dimensional...

### A New Approach to the Paperfolding Sequences

- Computer ScienceCiE
- 2015

In this paper we show how to re-derive known results about the paperfolding sequences, and obtain new ones, using a new approach using a decision method and some machine computation. We also obtain…

### Overlap-Free Words and Generalizations

- Chemistry
- 2007

"The research presented here was supported financially by the Natural Sciences
and Engineering Research Council of Canada (NSERC)."

## References

SHOWING 1-10 OF 24 REFERENCES

### Non-Repetitive Tilings

- MathematicsElectron. J. Comb.
- 2002

A two-dimensional version of Axel Thue's result, showing how to construct a rectangular tiling of the plane using 5 symbols which has the property that lines of tiles which are horizontal, vertical or have slope +1 or $-1$ contain no repetitions.

### Canonical Positions for the Factors in Paperfolding Sequences

- MathematicsTheor. Comput. Sci.
- 1994

### Infinite 0-1-sequences without long adjacent identical blocks

- MathematicsDiscret. Math.
- 1979

### Facteurs des suites de Rudin-Shapiro généralisées

- Mathematics
- 1994

\Integrating" paperfolding sequences yields generalized Rudin-Shapiro sequences. We study the factors (subwords) of these sequences, giving an (optimal) property of \half-synchronization" and a…

### The number of factors in a paperfolding sequence

- MathematicsBulletin of the Australian Mathematical Society
- 1992

We prove that the number of factors of length k in any paperfolding sequence is equal to 4k once k ≥ 7.

### Über unendliche Zeichenreihen

- Kra. Vidensk. Selsk. Skrifter. I. Mat. Nat. Kl. 1
- 1906