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 ...

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 ...

Large context problems (LCP) are useful in teaching the history of science. In this article we consider the brachistochrone problem in a context stretching from Euclid through the Bernoullis. We highlight a variety of ...

We show that Dejean’s conjecture holds for n ≥ 27. This brings the final resolution of the conjecture by the approach of Moulin Ollagnier within range of the computationally feasible.

The thesis begins by giving background in linear programming and Simplex methods. Topics covered include the duality theorem, Lemke's algorithm, and the pathological programs of Klee-Minty. Because of the bad behaviour ...

We perform an exact enumeration of the order-preserving maps of fences (zig-zags) and crowns (cycles). From this we derive asymptotic results.

For every pattern p over the alphabet {x, x^R, y, y^R}, we specify the least k such that p is k-avoidable.

We show that the number of ternary words of length n avoiding abelian cubes grows faster than r^n, where r = 2^{1/24}

Richomme asked the following question: what is the infimum of the real numbers α > 2 such that there exists an infinite word that avoids α-powers but contains arbitrarily large squares beginning at every position? We resolve ...

A graph is called well-covered if every maximal independent set has the same size. One generalization of independent sets in graphs is that of a fractional cover -- attach nonnegative weights to the vertices and require ...