Restricted generating trees for weak orderingsArticle
Authors: Daniel Birmajer ; Juan B. Gil ; David S. Kenepp ; Michael D. Weiner
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Daniel Birmajer;Juan B. Gil;David S. Kenepp;Michael D. Weiner
Motivated by the study of pattern avoidance in the context of permutations
and ordered partitions, we consider the enumeration of weak-ordering chains
obtained as leaves of certain restricted rooted trees. A tree of order $n$ is
generated by inserting a new variable into each node at every step. A node
becomes a leaf either after $n$ steps or when a certain stopping condition is
met. In this paper we focus on conditions of size 2 ($x=y$, $x<y$, or $x\le y$)
and several conditions of size 3. Some of the cases considered here lead to the
study of descent statistics of certain `almost' pattern-avoiding permutations.