Using the notion of series parallel interval order, we propose a unified setting to describe Dyck lattices and Tamari lattices (two well-known lattice structures on Catalan objects) in terms of basic notions of the theory of posets. As a consequence of our approach, we find an extremely simple proof of the fact that the Dyck order is a refinement of the Tamari one. Moreover, we provide a description of both the weak and the strong Bruhat order on 312-avoiding permutations, by recovering the proof of the fact that they are isomorphic to the Tamari and the Dyck order, respectively; our proof, which simplifies the existing ones, relies on our results on series parallel interval orders.
Swipe to navigate through the chapters of this book
Please log in to get access to this content
To get access to this content you need the following product:
- Catalan Lattices on Series Parallel Interval Orders
- Springer Basel
- Sequence number
Neuer Inhalt/© ITandMEDIA