Bijections on pattern avoiding inversion sequences and related objects

초록

The number of inversion sequences avoiding two patterns 101 and 102 is known to be the same as the number of permutations avoiding three patterns 2341, 2431, and 3241. This sequence also counts the number of Schr & ouml;der paths without triple descents, restricted bicolored Dyck paths, (101, 021)-avoiding inversion sequences, and weighted ordered trees. We provide bijections to integrate them together by introducing F-paths. Moreover, we define three kinds of statistics for each of the objects and count the number of each object with respect to these statistics. We also discuss direct sums of each object. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

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