Vladimir Dotsenko (Dublin):
Consecutive patterns in words, permutations and in trees
When dealing with combinatorics of words, saying "a consecutive
pattern in a word" is a fancy way of saying "a subword". For
permutations, it becomes more interesting: a permutation w occurs in
another permutation v as a consecutive pattern if v contains a subword
which is order-isomorphic to w. It turns out that both these topics
can be embedded into a common framework of pattern avoidance in trees.
I shall give an elementary introduction in those topics, formulate
some open problems, and explain why studying these questions is
natural for someone interested in algebra and algebraic topology. I
shall also briefly outline a method allowing to approach questions of
enumerative combinatorics for permutations using homological algebra.