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Partially ordered patterns and their combinatorial interpretations

Burstein, Alexander and Kitaev, Sergey (2008) Partially ordered patterns and their combinatorial interpretations. Pure Mathematics and Applications, 19 (2-3). pp. 27-38. ISSN 1218-4586

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Abstract

This paper is a continuation of the study of partially ordered patterns (POPs) introduced recently. We provide a general approach to code combinatorial objects using (POP-)restricted permutations. We give several examples of relations between permutations restricted by POPs and 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.