Currie, James D.; Rampersad, Narad(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
.
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 ...
Currie, James D.(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 ...
Allouche, Jean-Paul; Currie, James D.; Shallit, Jeffrey(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 ...
Currie, James D.(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 ...
Currie, James D.; Rampersad, Narad; Shallit, Jeffrey(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.
Currie, James D.; Rampersad, Narad(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 ...
Currie, James D.(The Electronic Journal of Combinatorics, 2016-05-27)
We solve a problem of Petrova, finalizing the classification of letter patterns avoidable by ternary square-free words; we show that there is a ternary square-free word avoiding letter pattern xyzxzyx. In fact, we characterize ...
Babb, J. C.; Dempster, C. J.; Wallis, R. J.(NRC Research Press, 1989-01)
A statistical regression model for rapid prediction of moisture content based on measurements of dielectric capacitance and test weight was developed for Eastern Canadian corn (Zea mays L.). For 336 samples of the 1986 ...
This paper examines the mathematical work of the French bishop, Nicole Oresme (c. 1323–1382), and his contributions towards the development of the concept of graphing functions and approaches to investigating infinite ...
Aveline's Hole is both one of the best-known sites with early human skeletal material in Britain and one of the most problematic in its history. First discovered and explored at the close of the 18th century, it yielded ...
Meiklejohn, Christopher; Babb, Jeff; Hiebert, Weldon(Landesamt für Denkmalpflege und Archäologie Sachsen-Anhalt, 2016)
Over the past decade we have focused on two interrelated topics within Mesolithic burial studies, the relationship between burial number and burial date, and the chronology of Mesolithic sites with burials. Related to this ...
Gosselin, Shonda(Journal of Combinatorial Designs, 2011-02-17)
In this paper, we examine the possible orders of t-subset-regular selfcomplementary
k-uniform hypergraphs, which form examples of large sets
of two isomorphic t-designs. We reformulate Khosrovshahi and Tayfeh-
Rezaie's ...
For an integer n and a prime p, let n.p/ D maxfi V pi divides ng. In this paper, we present
a construction for vertex-transitive self-complementary k-uniform hypergraphs of order
n for each integer n such that pn.p/ 1 ...
In 2007, Szymanski and Wojda proved that for positive integers n; k with k<n, a self-complementary
k-uniform hypergraph of order n exists if and only if
n/k is even. In
this paper, we characterize the cycle type of a ...
Gosselin, Shonda(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 ...