Daniel Birmajer ; Juan B. Gil ; David S. Kenepp ; Michael D. Weiner - Restricted generating trees for weak orderings

dmtcs:8350 - Discrete Mathematics & Theoretical Computer Science, March 21, 2022, vol. 24, no. 1 - https://doi.org/10.46298/dmtcs.8350
Restricted generating trees for weak orderings

Authors: 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.


    Volume: vol. 24, no. 1
    Section: Combinatorics
    Published on: March 21, 2022
    Accepted on: March 3, 2022
    Submitted on: August 11, 2021
    Keywords: Mathematics - Combinatorics,05A18

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