Chain lengths in the type $B$ Tamari lattice

TL;DR

This paper determines the maximum union of two chains in the type B Tamari lattice by extending methods from the classical type A case, incorporating a description specific to type B.

Contribution

It generalizes the techniques used for the classical Tamari lattice to the type B case, providing new insights into its combinatorial structure.

Findings

Largest union of two chains in type B Tamari lattice identified

Generalization of classical Tamari lattice techniques to type B

Enhanced understanding of the combinatorial structure of type B Tamari lattice

Abstract

We find the largest union of two chains in the type $B$ Tamari lattice by generalizing the techniques used for the classical (type $A$) Tamari lattice with a description of the type $B$ case due to Hugh Thomas.