DOAJ Open Access 2020

Oriented Flip Graphs and Noncrossing Tree Partitions

Alexander Garver Thomas McConville

Lihat Sumber DOI

Abstrak

Given a tree embedded in a disk, we define two lattices - the oriented flip graph of noncrossing arcs and the lattice of noncrossing tree partitions. When the interior vertices of the tree have degree 3, the oriented flip graph is equivalent to the oriented exchange graph of a type A cluster algebra. Our main result is an isomorphism between the shard intersection order of the oriented flip graph and the lattice of noncrossing tree partitions. As a consequence, we deduce a simple characterization of c-matrices of type A cluster algebras.

Topik & Kata Kunci

Mathematics

Penulis (2)

Alexander Garver

Thomas McConville

Format Sitasi

APA MLA BibTeX

Garver, A., McConville, T. (2020). Oriented Flip Graphs and Noncrossing Tree Partitions. https://doi.org/10.46298/dmtcs.6379

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.6379

Informasi Jurnal

Tahun Terbit: 2020
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.6379
Akses: Open Access ✓