WinnSpace at University of Winnipeg
http://winnspace.uwinnipeg.ca:80
The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 08 Dec 2019 08:43:55 GMT2019-12-08T08:43:55ZBinary Words Avoiding xxRx and Strongly Unimodal Sequences
http://hdl.handle.net/10680/1758
Binary Words Avoiding xxRx and Strongly Unimodal Sequences
Currie, James D.; Rampersad, Narad
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 growth of the number
of binary words avoiding the pattern xxRx. Curiously, the analysis for xxRx is much
simpler than that for xxxR. We derive our results by giving a bijection between the
set of binary words avoiding xxRx and a class of sequences closely related to the class
of “strongly unimodal sequences”.
Mon, 14 Sep 2015 00:00:00 GMThttp://hdl.handle.net/10680/17582015-09-14T00:00:00ZA ternary square-free sequence avoiding factors equivalent to abcacba
http://hdl.handle.net/10680/1756
A ternary square-free sequence avoiding factors equivalent to abcacba
Currie, James D.
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 all the (two-way) infinite ternary square-free words avoiding letter pattern xyzxzyx
-characterize the lexicographically least (one-way) infinite ternary square-free word avoiding letter pattern xyzxzyx
-show that the number of ternary square-free words of length n avoiding letter pattern xyzxzyx grows exponentially with
n.
Fri, 27 May 2016 00:00:00 GMThttp://hdl.handle.net/10680/17562016-05-27T00:00:00ZA family of formulas with reversal of high avoidability index
http://hdl.handle.net/10680/1755
A family of formulas with reversal of high avoidability index
Currie, James; Mol, Lucas; Rampersad, Narad
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 due to its size and the simple structure of its members. For each k ∈ {4,5}, there are several previously known avoidable formulas (without reversal) of avoidability index k, but they are small in number and they all have rather complex structure.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10680/17552017-01-01T00:00:00ZAvoidability index for binary patterns with reversal
http://hdl.handle.net/10680/1754
Avoidability index for binary patterns with reversal
Currie, James D.; Lafrance, Phillip
For every pattern p over the alphabet {x,x^R,y,y^R}, we specify the least k such that p is k-avoidable.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10680/17542017-01-01T00:00:00ZBinary words containing infinitely many overlaps
http://hdl.handle.net/10680/1753
Binary words containing infinitely many overlaps
Currie, James D.; Rampersad, Narad; Shallit, Jeffrey
We characterize the squares occurring in infinite overlap-free binary words and construct various \alpha power-free binary words containing infinitely many overlaps.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10680/17532006-01-01T00:00:00ZAttainable lengths for circular binary words avoiding k-powers
http://hdl.handle.net/10680/1752
Attainable lengths for circular binary words avoiding k-powers
Currie, James D.; Aberkane, Ali
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
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10680/17522005-01-01T00:00:00ZThe Number of Ternary Words Avoiding Abelian Cubes Grows Exponentially
http://hdl.handle.net/10680/1751
The Number of Ternary Words Avoiding Abelian Cubes Grows Exponentially
Currie, James; Rampersad, Narad; Aberkane, Ali
We show that the number of ternary words of length n avoiding abelian cubes grows
faster than r^n, where r = 2^{1/24}
Sat, 19 Jun 2004 00:00:00 GMThttp://hdl.handle.net/10680/17512004-06-19T00:00:00ZHorse and Herald: Posidippus' Equestrian Angelia
http://hdl.handle.net/10680/1750
Horse and Herald: Posidippus' Equestrian Angelia
Miller, Peter J
Posidippus’ epigrams for equestrian victors (the Hippika, AB 71–88) build on epinician convention by maintaining the central role of the herald’s proclamation— the angelia—in the representation of athletic achievement. In a few of these epigrams, however, Posidippus embeds the horse itself in postvictory rituals. For example, the horse brings the crown to the victor, replacing the figure of the herald who announced and crowned victors; or, in a narrative of the race’s aftermath, the horse, incredibly, chooses the victor. Posidippus’ horses, therefore, act as causal agents for the glory of their owners, and his detailed descriptions transform the horse from flesh-and-blood equine to everlasting (literary) monument.
Les épigrammes de Posidippe sur les victoires équestres (les Hippiques, 71-88 A.-B.) s’appuient sur une convention poétique propre aux épinicies qui maintient le rôle de la proclamation du héraut – l’angelia – dans la représentation de la réussite athlétique. Cependant, dans quelques-unes de ces épigrammes, Posidippe intègre le cheval lui-même au rituel marquant la victoire. Par exemple, le cheval apporte la couronne au vainqueur en remplacement de la figure du héraut qui annonce et couronne les vainqueurs ; ou encore, dans le récit de l’après-course, le cheval choisit, de façon surprenante, le vainqueur. Les chevaux de Posidippe interviennent donc en tant qu’agents causaux dans la gloire de leur propriétaire. Ses descriptions détaillées transforment ainsi l’être de chair et de sang qu’est le cheval en un monument (littéraire) éternel.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10680/17502019-01-01T00:00:00ZMillennial fire history reconstruction in the boreal forest of south-central Canada using lake-sediment charcoal, tree-ring and archival records
http://hdl.handle.net/10680/1749
Millennial fire history reconstruction in the boreal forest of south-central Canada using lake-sediment charcoal, tree-ring and archival records
Waito, Justin M.
The Canadian boreal forest has been developing since the end of the last glaciation approximately 10,000 years ago. During this time, fire has modified the development of the forest by altering species distribution, stand structure and forest regeneration. With future climate changes, the fire frequency and annual area burned (AAB) are expected to increase with increasing temperatures. It remains unclear what effect this increase in fire frequency will have on the forest. Current projections of future fire are often based on relatively short environmental records and longer records are needed to capture variability in fire occurrence over millennia. In this study, a multi-millennial fire history was reconstructed for eight lakes from the Lake of the Woods Ecoregion (LWE) within the boreal forest of central North America using a combination of archival, tree-ring and lake sediment charcoal records. The archival record provided fire dates and area burned information for the period 1920 to 2010. A tree-ring fire history reconstruction was developed around eight lakes for the period 1690-2010 from stand initiation dates and fire scars. The fire history reconstruction was extended through lake sediment charcoal records obtained from overlapping sediment cores collected from eight lakes. For each lake, the sediment fire history reconstruction was obtained from macroscopic charcoal particles with an area >150 micrometers. Calculation of the Charcoal Accumulation Rate (CHAR) and subsequent peak analysis of the CHAR record allowed for the examination of changes in fire regime dating back to 2500 BP (500 BCE).
The archival and tree-ring records revealed recent large fires (>200 ha) in 1948, 1980 and 1989. An additional 17 fires were identified by the fire-scar record. Fire events in 1805, 1840, 1863, and the 1890’s were identified in numerous locations around multiple lakes suggesting that they were of large extents. In accordance with the tree-ring record, the CHAR peak record generally identified the major fires, with identification becoming less accurate for smaller fires and those in close succession. The CHAR record also tended to lag behind fires identified from tree-ring records by several decades. Within the LWE, the long-term charcoal record revealed that CHAR was higher for each lake in the earlier portion of the record followed by a progressive decrease towards the more recent record. Multi-millennial fluctuations in CHAR suggested that modern temperature increases could lead to higher fire frequency than that observed over the last two millennia.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10680/17492016-01-01T00:00:00ZThe metric dimension and metric independence of a graph
http://hdl.handle.net/10680/1746
The metric dimension and metric independence of a graph
Currie, James; Oellerman, Ortrud R.
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 resolved by some vertex of S. The minimum cardinality of a
resolving set for G is called the metric dimension of G. The problem of
nding the metric dimension of a graph is formulated as an integer pro-
gramming problem. It is shown how a relaxation of this problem leads
to a linear programming problem and hence to a fractional version of
the metric dimension of a graph. The linear programming dual of this
problem is considered and the solution to the corresponding integer
programming problem is called the metric independence of the graph.
It is shown that the problem of deciding whether, for a given graph
G, the metric dimension of G equals its metric independence is NP-
complete. Trees with equal metric dimension and metric independence
are characterized. The metric independence number is established for
various classes of graphs.
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10680/17462001-01-01T00:00:00Z