Refining the bijections among ascent sequences, (2+2)-free posets, integer matrices and pattern-avoiding permutations
نویسندگان
چکیده
منابع مشابه
(2+2)-free Posets, Ascent Sequences and Pattern Avoiding Permutations
We present bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (2 + 2)-free posets and a certain class of involutions (or chord diagrams), already appeared in the literature, but were apparently not known to be equinumerous. We present a direct bijection between them. The third class is a family of permutations defined in terms of a new type of pattern....
متن کاملUnlabeled (2+ 2)-free Posets, Ascent Sequences and Pattern Avoiding Permutations
We present bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (2 + 2)-free posets and a certain class of chord diagrams (or involutions), already appear in the literature. The third one is a class of permutations, defined in terms of a new type of pattern. An attractive property of these patterns is that, like classical patterns, they are closed under ...
متن کاملGood sequences, bijections and permutations
In the present paper we study general properties of good sequences by means of a powerful and beautiful tool of combinatorics—the method of bijective proofs. A good sequence is a sequence of positive integers k = 1, 2, . . . such that the element k occurs before the last occurrence of k + 1. We construct two bijections between the set of good sequences of length n and the set of permutations of...
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We show that there are n! matchings on 2n points without socalled left (neighbor) nestings. We also define a set of naturally labeled (2+2)free posets and show that there are n! such posets on n elements. Our work was inspired by Bousquet-Mélou, Claesson, Dukes and Kitaev [J. Combin. Theory Ser. A. 117 (2010) 884–909]. They gave bijections between four classes of combinatorial objects: matching...
متن کاملOn 021-Avoiding Ascent Sequences
Ascent sequences were introduced by Bousquet-Mélou, Claesson, Dukes and Kitaev in their study of (2 + 2)-free posets. An ascent sequence of length n is a nonnegative integer sequence x = x1x2 . . . xn such that x1 = 0 and xi ≤ asc(x1x2 . . . xi−1) + 1 for all 1 < i ≤ n, where asc(x1x2 . . . xi−1) is the number of ascents in the sequence x1x2 . . . xi−1. We let An stand for the set of such seque...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2019
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2019.05.007