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Enumerations of Permutations Simultaneously Avoiding a Vincular and a Covincular Pattern of Length 3

Enumerations of Permutations Simultaneously Avoiding a Vincular and a Covincular Pattern of Length 3


Titill: Enumerations of Permutations Simultaneously Avoiding a Vincular and a Covincular Pattern of Length 3
Höfundur: Bean, Christian
Claesson, Anders   orcid.org/0000-0001-5797-8673
Úlfarsson, Henning Arnór
Útgáfa: 2017
Tungumál: Enska
Umfang: 17.7.6
Háskóli/Stofnun: Háskólinn í Reykjavík
Reykjavik University
Háskóli Íslands
University of Iceland
Svið: Verkfræði- og náttúruvísindasvið (HÍ)
School of Engineering and Natural Sciences (UI)
Deild: Tölvunarfræðideild (HR)
School of Computer Science (RU)
Raunvísindastofnun (HÍ)
Science Institute (UI)
Birtist í: Journal of Integer Sequences;20
ISSN: 1530-7638
Efnisorð: Tölvunarfræði; Stærðfræði
URI: https://hdl.handle.net/20.500.11815/532

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Tilvitnun:

Christian Bean , Anders Claesson , and Henning Ulfarsson. (2017). Enumerations of Permutations Simultaneously Avoiding a Vincular and a Covincular Pattern of Length 3, Journal of Integer Sequences, Vol. 20, article 17.7.6

Útdráttur:

Vincular and covincular patterns are generalizations of classical patterns allowing restrictions on the indices and values of the occurrences in a permutation. In this paper we study the integer sequences arising as the enumerations of permutations simultaneously avoiding a vincular and a covincular pattern, both of length 3, with at most one restriction. We see familiar sequences, such as the Catalan and Motzkin numbers, but also some previously unknown sequences which have close links to other combinatorial objects such as lattice paths and integer partitions. Where possible we include a generating function for the enumeration. One of the cases considered settles a conjecture by Pudwell (2010) on the Wilf-equivalence of barred patterns. We also give an alternative proof of the classic result that permutations avoiding 123 are counted by the Catalan numbers.

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