DOAJ Open Access 2014

Newton Polytopes of Cluster Variables of Type $A_n$

Adam Kalman

Lihat Sumber DOI

Abstrak

We study Newton polytopes of cluster variables in type $A_n$ cluster algebras, whose cluster and coefficient variables are indexed by the diagonals and boundary segments of a polygon. Our main results include an explicit description of the affine hull and facets of the Newton polytope of the Laurent expansion of any cluster variable, with respect to any cluster. In particular, we show that every Laurent monomial in a Laurent expansion of a type $A$ cluster variable corresponds to a vertex of the Newton polytope. We also describe the face lattice of each Newton polytope via an isomorphism with the lattice of elementary subgraphs of the associated snake graph.

Topik & Kata Kunci

Mathematics

Penulis (1)

Adam Kalman

Format Sitasi

APA MLA BibTeX

Kalman, A. (2014). Newton Polytopes of Cluster Variables of Type $A_n$. https://doi.org/10.46298/dmtcs.2387

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.2387

Informasi Jurnal

Tahun Terbit: 2014
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.2387
Akses: Open Access ✓