Bijections on pattern avoiding inversion sequences and related objects.

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 Schröder 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. [ABSTRACT FROM AUTHOR]