Using homological duality in consecutive pattern avoidance

Details Using homological duality in consecutive pattern avoidance Using homological duality in consecutive pattern avoidance

2010-09-27

arxiv.org/abs/1009.5308v1

Mathematics

Combinatorics

12 pages, 1 figure

Scientific paper

Using the approach suggested in [arXiv:1002.2761] we present below a sufficient condition guaranteeing that two collections of patterns of permutations have the same exponential generating functions for the number of permutations avoiding elements of these collections as consecutive patterns. In short, the coincidence of the latter generating functions is guaranteed by a length-preserving bijection of patterns in these collections which is identical on the overlappings of pairs of patterns where the overlappings are considered as unordered sets. Our proof is based on a direct algorithm for the computation of the inverse generating functions. As an application we present a large class of patterns where this algorithm is fast and, in particular, allows to obtain a linear ordinary differential equation with polynomial coefficients satisfied by the inverse generating function.

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