PARTIALLY ORDERED GENERALIZED PATTERNS AND k - ARY
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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...
متن کاملKitaev And
Recently, Kitaev [Ki2] introduced partially ordered generalized patterns (POGPs) in the symmetric group, which further generalize the generalized permutation patterns introduced by Babson and Steingŕımsson [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, ex...
متن کاملPartially Ordered Patterns and Compositions
A partially ordered (generalized) pattern (POP) is a generalized pattern some of whose letters are incomparable, an extension of generalized permutation patterns introduced by Babson and Steingŕımsson. POPs were introduced in the symmetric group by Kitaev [19, 21], and studied in the set of k-ary words by Kitaev and Mansour [22]. Moreover, Kitaev et al. [23] introduced segmented POPs in composi...
متن کامل. C O ] 1 O ct 2 00 6 PARTIALLY ORDERED PATTERNS AND COMPOSITIONS
A partially ordered (generalized) pattern (POP) is a generalized pattern some of whose letters are incomparable, an extension of generalized permutation patterns introduced by Babson and Steingŕımsson. POPs were introduced in the symmetric group by Kitaev [19, 21], and studied in the set of k-ary words by Kitaev and Mansour [22]. Moreover, Kitaev et al. [23] introduced segmented POPs in composi...
متن کاملAVOIDANCE OF PARTIALLY ORDERED PATTERNS OF THE FORM k-σ-k
Sergey Kitaev [4] has shown that the exponential generating function for permutations avoiding the generalized pattern σ-k, where σ is a pattern without dashes and k is one greater than the largest element in σ, is determined by the exponential generating function for permutations avoiding σ. We show that the exponential generating function for permutations avoiding the partially ordered patter...
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