Due to the condition of the original material, there are unavoidable flaws in this reproduction. We have made every effort to provide you with the best copy available. If you are dissatisfied with this product and find it unusable, please contact Document Services as soon as possible. Thank you.

Due to the condition of the original material, there are unavoidable flaws in this reproduction. We have made every effort possible to provide you with the best copy available. If you are dissatisfied with this product and find it unusable, please contact Document Services as soon as possible.

We present an algorithm which produces, in some cases, infinite words avoiding both large fractional repetitions and a given set of finite words. We use this method to show that all the ternary patterns whose avoidability index was left open in Cassaigne’s thesis are 2-avoidable. We also prove that there exist exponentially many 7 4 + -free ternary words and 7 5 + -free 4-ary words. Finally we ...

A basic result in Ramsey theory states that any tournament contains a “large” transitive subgraph. Since transitive tournaments contain only transitive subgraphs, it is natural to ask which subgraphs must appear in any large tournament that is “far” from being transitive. One result of this type was obtained by Fox and Sudakov who characterized the tournaments that appear in any tournament that...

Let Tk be a family of all k-vertex trees. For T ⊆ Tk and a tree T , we write T → T if T contains at least one of the trees from T as a subtree, we write T 6→ T otherwise. Let ex(T ) be the smallest integer n, if such exists, such that for any tree T on at least n vertices T → T . It is shown that min{ex(T ) : T ⊆ Tk, |T | = q} = 2 log q−1 , where logq−1 is the q− 1 times iterated logarithm. In ...

We investigate both the locus of ambiguity in the architecture of language and the origin of ambiguity in natural communication. We 1) locate ambiguity at the externalization branch of language, 2) provide a rigorous, general definition of ambiguity through the concept of logical irreversibility, quantifying the amount of ambiguity within the framework of Shannon’s information theory, and 3) pr...

For integers a1, . . . , an > 0 and k > 1, let Lk+2(a1, . . . , an) denote the set of permutations of {1, . . . , a1 + · · · + an} whose descent set is contained in {a1, a1 + a2, . . . , a1+ · · ·+an−1}, and which avoids the pattern 12 . . . (k+2). We exhibit some bijections between such sets, most notably showing that #Lk+2(a1, . . . , an) is symmetric in the ai and is in fact Schur-concave. T...