On 021-Avoiding Ascent Sequences

Chen, William Y. C.; Dai, Alvin Y. L.; Dokos, Theodore; Dwyer, Tim; Sagan, Bruce E.

doi:10.48550/arxiv.1206.2849

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“…The paper [14] has been followed by a great number of papers on these and bijectively related combinatorial objects, with no end in sight. The study of pattern avoidance by the ascent sequences in their own right was recently initiated [24] and has been furthered in [20,35,51], each of which proves some of the conjectures made in [24]. We say that two patterns are Wilf equivalent, and belong to the same Wilf class, if, for each n, the same number of permutations of length n avoids each.…”

Section: -2-4-1mentioning

confidence: 96%

Some open problems on permutation patterns

Steingrı́msson

2013

Surveys in Combinatorics 2013

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This is a brief survey of some open problems on permutation patterns, with an emphasis on subjects not covered in the recent book by Kitaev, Patterns in Permutations and words. I first survey recent developments on the enumeration and asymptotics of the pattern 1324, the last pattern of length 4 whose asymptotic growth is unknown, and related issues such as upper bounds for the number of avoiders of any pattern of length k for any given k. Other subjects treated are the Möbius function, topological properties and other algebraic aspects of the poset of permutations, ordered by containment, and also the study of growth rates of permutation classes, which are containment closed subsets of this poset.2 In this section I write classical patterns with dashes between all pairs of adjacent letters, to distinguish them from other vincular and bivincular patterns. In later sections, I will write classical patterns in the classical way, without any dashes, to keep the notation less cumbersome.

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Section: -2-4-1mentioning

confidence: 96%

Some open problems on permutation patterns

Steingrı́msson

2013

Surveys in Combinatorics 2013

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On 021-Avoiding Ascent Sequences

Cited by 1 publication

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Some open problems on permutation patterns

Some open problems on permutation patterns

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