Clark has defined the notion of n-avoidance basis which contains the avoidable formulas with at most n variables that are closest to be unavoidable in some sense. The family Ci of circular formulas is such that C1 = AA, C2 = ABA.BAB, C3 = ABCA.BCAB.CABC and so on. For every i 6 n, the n-avoidance basis contains Ci. Clark showed that the avoidability index of every circular formula and of every ...

This article presents a model for Internet portal management. The model allows portal implementers to monitor and reflect on their portal implementation process and to identify appropriate strategies to improve their community building efforts. The portal management model (PMM) is a lifecycle model that contains four stages. Each stage is identified and described by a number of characteristics ...

In this paper we study pattern avoidance for affine permutations. In particular, we show that for a given pattern p, there are only finitely many affine permutations in S̃n that avoid p if and only if p avoids the pattern 321. We then count the number of affine permutations that avoid a given pattern p for each p in S3, as well as give some conjectures for the patterns in S4.

We show that every avoidable pattern can be avoided by an infinite sequence of palindromes over a fixed finite alphabet. © 2009 Elsevier B.V. All rights reserved.

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

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A set of words over a finite alphabet is called an unavoidable set if every word of sufficiently long length must contain some word from this set as a subword. Motivated by a theorem from automata theory, we introduce the notion of an almost unavoidable set and prove certain asymptotic estimates for the size of almost unavoidable sets of uniform length.