Browsing Department of Mathematics and Statistics by Author "Currie, James D."
Now showing items 1-20 of 26
-
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 -
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. -
Avoiding three consecutive blocks of the same size and same sum
(Association of Computing Machinery, 2014-04)We show that there exists an infinite word over the alphabet {0,1,3,4} containing no three consecutive blocks of the same size and the same sum. This answers an open problem of Pirillo and Varricchio from1994. -
Binary Words Avoiding xxRx and Strongly Unimodal Sequences
(2015-09-14)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 ... -
Binary Words Containing Infinitely Many Overlaps
(The Electronic Journal of Combinatorics, 2006-09-22)We characterize the squares occurring in infinite overlap-free binary words and construct various α power-free binary words containing infinitely many overlaps. -
Characterization of the lengths of binary circular words containing no squares other than 00, 11, and 0101
(2020-05-19)We characterize exactly the lengths of binary circular words containing no squares other than 00, 11, and 0101. -
Class Numbers and Biquadratic Reciprocity
(Cambridge University Press, 1982) -
Combinatorics and Algorithmics of Strings
(Dagstuhl Publishing, 2014-03-09)Strings (aka sequences or words) form the most basic and natural data structure. They occur whenever information is electronically transmitted (as bit streams), when natural language text is spoken or written down (as words ... -
Counting endomorphisms of crown-like orders
(Springer, 2002-12)The authors introduce the notion of crown-like orders and introduce powerful tools for counting the endomorphisms of orders of this type. -
Cubefree words with many squares
(Discrete Mathematics and Theoretical Computer Science, 2014-05-13)We construct infinite cubefree binary words containing exponentially many distinct squares of length n . We also show that for every positive integer n , there is a cubefree binary square of length 2n. -
A direct proof of a result of Thue
(Utilitas Mathematica, 1984) -
Extremal Infinite Overlap-Free Binary Words
(The Electronic Journal of Combinatorics, 1998-05-03)Let t be the infinite fixed point, starting with 1, of the morphism μ:0→01, 1→10. An infinite word over {0,1} is said to be overlap-free if it contains no factor of the form axaxa, where a∈{0,1} and x∈{0,1}∗. We prove that ... -
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 ... -
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 ... -
Growth rate of binary words avoiding xxxR
(Elsevier, 2016-01)Abstract Consider the set of those binary words with no non-empty factors of the form xxx^R. Du, Mousavi, Schaeffer, and Shallit asked whether this set of words grows polynomially or exponentially with length. In this ... -
Least Periods of Factors of Infinite Words
(EDP Sciences, 2009)We show that any positive integer is the least period of a factor of the Thue-Morse word. We also characterize the set of least periods of factors of a Sturmian word. In particular, the corresponding set for the Fibonacci ... -
Non-Repetitive Tilings
(The Electronic Journal of Combinatorics, 2002-07-03)In 1906 Axel Thue showed how to construct an infinite non-repetitive (or square-free) word on an alphabet of size 3. Since then this result has been rediscovered many times and extended in many ways. We present a two-dimensional ... -
A Note on Antichains of Words
(The Electronic Journal of Combinatorics, 1995-10-14)We can compress the word 'banana' as xyyz, where x= 'b', y= 'an',z= 'a'. We say that 'banana' encounters yy. Thus a 'coded' version of yy shows up in 'banana'. The relation 'u encounters w' is transitive, and thus generates ... -
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 ...
