Geodesic
Restricted generating trees for weak orderings
Discrete mathematics & theoretical computer science, Tome 24 (2022) no. 1.

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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, 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.
DOI : 10.46298/dmtcs.8350
Classification : 05A05, 05A15, 05A18, 05C05, 06A07 
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Birmajer, Daniel; Gil, Juan B.; Kenepp, David S.; Weiner, Michael D. Restricted generating trees for weak orderings. Discrete mathematics & theoretical computer science, Tome 24 (2022) no. 1. doi : 10.46298/dmtcs.8350. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.8350/

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