Now showing items 1-10 of 39
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 ...
Counting endomorphisms of crown-like orders
The authors introduce the notion of crown-like orders and introduce powerful tools for counting the endomorphisms of orders of this type.
Characterization of the lengths of binary circular words containing no squares other than 00, 11, and 0101
We characterize exactly the lengths of binary circular words containing no squares other than 00, 11, and 0101.
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 ...
There are Ternary Circular Square-Free Words of Length n for n ≥ 18
(The Electronic Journal of Combinatorics, 2002-10-11)
There are circular square-free words of length n on three symbols for n≥18. This proves a conjecture of R. J. Simpson.
The number of order–preserving maps of fences and crowns
We perform an exact enumeration of the order-preserving maps of fences (zig-zags) and crowns (cycles). From this we derive asymptotic results.
Binary Words Avoiding xxRx and Strongly Unimodal Sequences
In previous work, Currie and Rampersad showed that the growth of the number of binary words avoiding the pattern xxxR was intermediate between polynomial and exponential. We now show that the same result holds for the ...
The metric dimension and metric independence of a graph
(The Charles Babbage Research Centre, 2001)
A vertex x of a graph G resolves two vertices u and v of G if the distance from x to u does not equal the distance from x to v. A set S of vertices of G is a resolving set for G if every two distinct vertices of G are ...
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.