منابع مشابه
On 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...
متن کاملAscent Sequences Avoiding Pairs of Patterns
Ascent sequences were introduced by Bousquet-Melou et al. in connection with (2+2)-avoiding posets and their pattern avoidance properties were first considered by Duncan and Steingŕımsson. In this paper, we consider ascent sequences of length n avoiding two patterns of length 3, and we determine an exact enumeration for 16 different pairs of patterns. Methods include simple recurrences, bijecti...
متن کامل(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 کاملGeneralized ballot sequences are ascent sequences
Ascent sequences were introduced by the author (in conjunction with others) to encode a class of permutations that avoid a single lengththree bivincular pattern, and were the central object through which other combinatorial correspondences were discovered. In this note we prove the non-trivial fact that generalized ballot sequences are ascent sequences. Ascent sequences were introduced in [1] t...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2013
ISSN: 1077-8926
DOI: 10.37236/2472