منابع مشابه
Pattern Avoiding Permutations
We establish a bijection from the set of all permutations (of a given length) that avoid a pattern q and a context-sensitive language.
متن کاملAlternating, Pattern-Avoiding Permutations
We study the problem of counting alternating permutations avoiding collections of permutation patterns including 132. We construct a bijection between the set Sn(132) of 132-avoiding permutations and the set A2n+1(132) of alternating, 132avoiding permutations. For every set p1, . . . , pk of patterns and certain related patterns q1, . . . , qk, our bijection restricts to a bijection between Sn(...
متن کاملPattern-Avoiding Permutations
are three distinct patterns. The first is known as a classical pattern (dashes in all − 1 slots); the third is also known as a consecutive pattern (no dashes in any slots). Some authors call ̃ a “generalized pattern” and use the word “pattern” exclusively for what we call “classical patterns”. Let = 1 2 · · · be a permutation on {1 2 }, where ≥ . We say that contains ̃...
متن کاملPattern-avoiding alternating words
Abstract. A word w = w1w2 · · ·wn is alternating if either w1 < w2 > w3 < w4 > · · · (when the word is up-down) or w1 > w2 < w3 > w4 < · · · (when the word is down-up). In this paper, we initiate the study of (pattern-avoiding) alternating words. We enumerate up-down (equivalently, down-up) words via finding a bijection with order ideals of a certain poset. Further, we show that the number of 1...
متن کاملOn Pattern-Avoiding Partitions
A set partition of size n is a collection of disjoint blocks B1, B2, . . . , Bd whose union is the set [n] = {1, 2, . . . , n}. We choose the ordering of the blocks so that they satisfy minB1 < minB2 < · · · < minBd. We represent such a set partition by a canonical sequence π1, π2, . . . , πn, with πi = j if i ∈ Bj. We say that a partition π contains a partition σ if the canonical sequence of π...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2018
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2018.07.006