Segmental partially ordered generalized patterns

Segmental partially ordered generalized patterns

We continue the study of partially ordered generalized patterns (POGPs) considered in [9] for permutations and in [10] for words. We deal with segmented POGPs (SPOGPs). We state some general results and treat a number of patterns of length 4. We prove a result from [8] in a much simpler way and also establish a connection between SPOGPs and walks on lattice points starting from the origin and r...

Segmented Partially Ordered Generalized Patterns

We continue the study of partially ordered generalized patterns (POGPs) considered in [9] for permutations and in [10] for words. We deal with segmented POGPs (SPOGPs). We state some general results and treat a number of patterns of length 4. We prove a result from [8] in a much simpler way and also establish a connection between SPOGPs and walks on lattice points starting from the origin and r...

PARTIALLY ORDERED GENERALIZED PATTERNS AND k - ARY

Partially Ordered Generalized Patterns and Their Combinatorial Interpretations

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 term...

Partially Ordered Generalized Patterns and k-ary Words

Recently, Kitaev [9] introduced partially ordered generalized patterns (POGPs) in the symmetric group, which further generalize the generalized permutation patterns introduced by Babson and Steingrı́msson [1]. 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, exten...