Pattern formation on trees

Update on Wood Formation in Trees Wood Formation in Trees

Wood is the most important natural and endlessly renewable source of energy and therefore has a major future role as an environmentally cost-effective alternative to burning fossils fuels. The major role of wood is not only the provision of energy but also the provision of energy-sufficient material for our buildings and many other products. In addition, developing wood cells represent one of t...

Linear pattern matching on sparse suffix trees

Packing several characters into one computer word is a simple and natural way to compress the representation of a string and to speed up its processing. Exploiting this idea, we propose an index for a packed string, based on a sparse suffix tree [8] with appropriately defined suffix links. Assuming, under the standard unit-cost RAM model, that a word can store up to logσ n characters (σ the alp...

Pattern formation on large domains

Pattern avoidance in binary trees

This paper introduces the notion of pattern avoidance in binary trees. We provide an algorithm for computing the generating function that counts the number of n-leaf binary trees avoiding a given binary tree pattern t. Equipped with this counting mechanism, we study the analogue of Wilf equivalence in which two tree patterns are equivalent if the respective trees that avoid them are equinumerou...

Pattern Avoidance in Labelled Trees

We discuss a new notion of pattern avoidance motivatedby operad theory: pattern avoidance in planar labelled trees. It is a generalisation of various types of consecutive pattern avoidance studied before: consecutive patterns in words, permutations, colouredpermutations, etc. ThenotionofWilf equivalence for patterns in permutations admits a straightforward generalisation for (sets of) tree patt...