Vincular Pattern Posets and the Möbius Function of the Quasi-Consecutive Pattern Poset
نویسندگان
چکیده
منابع مشابه
The Möbius Function of the Consecutive Pattern Poset
An occurrence of a consecutive permutation pattern p in a permutation π is a segment of consecutive letters of π whose values appear in the same order of size as the letters in p. The set of all permutations forms a poset with respect to such pattern containment. We compute the Möbius function of intervals in this poset. For most intervals our results give an immediate answer to the question. I...
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We introduce a formal definition of a pattern poset which encompasses several previously studied posets in the literature. Using this definition we present some general results on the Möbius function and topology of such pattern posets. We prove our results using a poset fibration based on the embeddings of the poset, where embeddings are representations of occurrences. We show that the Möbius ...
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The consecutive pattern poset is the infinite partially ordered set of all permutations where σ ≤ τ if τ has a subsequence of adjacent entries in the same relative order as the entries of σ. We study the structure of the intervals in this poset from topological, poset-theoretic, and enumerative perspectives. In particular, we prove that all intervals are rank-unimodal and strongly Sperner, and ...
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We use discrete Morse theory to provide another proof of Bernini, Ferrari, and Steingrímsson’s formula for the Möbius function of the consecutive pattern poset. In addition, we are able to determine the homotopy type of this poset. Earlier, Björner determined the Möbius function and homotopy type of factor order and the results are remarkably similar to those in the pattern case. In his thesis,...
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We introduce the notion of pattern in the context of lattice paths, and investigate it in the specific case of Dyck paths. Similarly to the case of permutations, the pattern-containment relation defines a poset structure on the set of all Dyck paths, which we call the Dyck pattern poset. Given a Dyck path P , we determine a formula for the number of Dyck paths covered by P , as well as for the ...
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ژورنال
عنوان ژورنال: Annals of Combinatorics
سال: 2017
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-017-0364-y