Rational generating series for affine permutation pattern avoidance
نویسندگان
چکیده
منابع مشابه
Algebraic and Affine Pattern Avoidance
We investigate various connections between the 0Hecke monoid, Catalan monoid, and pattern avoidance in permutations, providing new tools for approaching pattern avoidance in an algebraic framework. In particular, we characterize containment of a class of ‘long’ patterns as equivalent to the existence of a corresponding factorization. We then generalize some of our constructions to the affine se...
متن کاملEnumerating Pattern Avoidance for Affine Permutations
In this paper we study pattern avoidance for affine permutations. In particular, we show that for a given pattern p, there are only finitely many affine permutations in S̃n that avoid p if and only if p avoids the pattern 321. We then count the number of affine permutations that avoid a given pattern p for each p in S3, as well as give some conjectures for the patterns in S4.
متن کاملExtended Abstract for Enumerating Pattern Avoidance for Affine Permutations
In this paper we study pattern avoidance for affine permutations. In particular, we show that for a given pattern p, there are only finitely many affine permutations in S̃n that avoid p if and only if p avoids the pattern 321. We then count the number of affine permutations that avoid a given pattern p for each p in S3, as well as give some conjectures for the patterns in S4. This paper is just ...
متن کاملReduced Decompositions with One Repetition and Permutation Pattern Avoidance
In 2007, Tenner established a connection between pattern avoidance in permutations and the Bruhat order on permutations by showing that the downset of a permutation in the Bruhat order is a Boolean algebra if and only if the permutation is 3412 and 321 avoiding. Tenner mentioned, but did not prove, that if the permutation is 321 avoiding and contains exactly one 3412 pattern, or if the permutat...
متن کاملFurther Applications of a Power Series Method for Pattern Avoidance
Abstract. In combinatorics on words, a word w over an alphabet Σ is said to avoid a pattern p over an alphabet ∆ if there is no factor x of w and no non-erasing morphism h from ∆∗ to Σ∗ such that h(p) = x. Bell and Goh have recently applied an algebraic technique due to Golod to show that for a certain wide class of patterns p there are exponentially many words of length n over a 4-letter alpha...
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ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2016
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2016.v7.n1.a3