TL;DR
This paper introduces Baxter posets, a new family of combinatorial objects linked to Baxter numbers, and explores their properties and connections to diagonal rectangulations and Baxter permutations.
Contribution
It defines Baxter posets, proves their enumeration by Baxter numbers, and describes methods to derive related permutations from these posets.
Findings
Baxter posets are counted by Baxter numbers.
Baxter posets are the adjacency posets of diagonal rectangulations.
Methods are provided to obtain Baxter and twisted Baxter permutations from Baxter posets.
Abstract
We define a family of combinatorial objects, which we call Baxter posets. We prove that Baxter posets are counted by the Baxter numbers by showing that they are the adjacency posets of diagonal rectangulations. Given a diagonal rectangulation, we describe the cover relations in the associated Baxter poset. Given a Baxter poset, we describe a method for obtaining the associated Baxter permutation and the associated twisted Baxter permutation.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Topics in Algebra · Algebraic structures and combinatorial models