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Partially ordered generalized patterns and their combinatorial interpretation

Burstein, Alexander and Kitaev, Sergey (2005) Partially ordered generalized patterns and their combinatorial interpretation. In: The Third International Conference on Permutation Patterns, 2005-03-07 - 2005-03-11, University of Florida.

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Abstract

This paper is a continuation of the study of partially ordered generalized patterns (POGPs) considered in [6, 7, 8]. We provide two general approaches: one to obtain connections between restricted permutations and other combinatorial structures, and one to treat the avoidance problems for words in case of segmented patterns. The former approach is related to coding combinatorial objects in terms of restricted permutations. We provide several examples of relations of our objects to other combinatorial structures, such as labeled graphs, walks, binary vectors, and others. Also, we show how restricted permutations are related to Cartesian products of certain objects.