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arXiv · 2108.04302

Restricted generating trees for weak orderings

Daniel Birmajer·Juan B. Gil·David S. Kenepp·Michael D. Weiner
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Abstract

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.

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Daniel Birmajer, Juan B. Gil, David S. Kenepp, Michael D. Weiner. 2021-08-09. Restricted generating trees for weak orderings. https://doi.org/10.46298/dmtcs.8350

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