Partially Ordered generalized patterns and k-ary words

Details Partially Ordered generalized patterns and k-ary words Partially Ordered generalized patterns and k-ary words

2002-10-02

arxiv.org/abs/math/0210023v1

Mathematics

Combinatorics

9 pages

Scientific paper

Recently, Kitaev [Ki2] introduced partially ordered generalized patterns (POGPs) in the symmetric group, which further generalize the generalized permutation patterns introduced by Babson and Steingr\'imsson [BS]. A POGP p is a GP some of whose letters are incomparable. In this paper, we study the generating functions (g.f.) for the number of k-ary words avoiding some POGPs. We give analogues, extend and generalize several known results, as well as get some new results. In particular, we give the g.f. for the entire distribution of the maximum number of non-overlapping occurrences of a pattern p with no hyphens (that allowed to have repetition of letters), provided we know the g.f. for the number of k-ary words that avoid p.

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