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Publications Influence

Positivity for cluster algebras from surfaces

- Gregg Musiker, R. Schiffler, L. Williams
- Mathematics
- 3 June 2009

We give combinatorial formulas for the Laurent expansion of any cluster variable in any cluster algebra coming from a triangulated surface (with or without punctures), with respect to an arbitrary… Expand

161 19- PDF

Bases for cluster algebras from surfaces

- Gregg Musiker, R. Schiffler, L. Williams
- Mathematics
- 19 October 2011

We construct two bases for each cluster algebra coming from a triangulated surface without punctures. We work in the context of a coefficient system coming from a full-rank exchange matrix, such as… Expand

107 11- PDF

Cluster expansion formulas and perfect matchings

- Gregg Musiker, R. Schiffler
- Mathematics
- 20 October 2008

We study cluster algebras with principal coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these… Expand

64 9- PDF

Linear systems on tropical curves

- C. Haase, Gregg Musiker, J. Yu
- Mathematics
- 21 September 2009

A tropical curve Γ is a metric graph with possibly unbounded edges, and tropical rational functions are continuous piecewise linear functions with integer slopes. We define the complete linear system… Expand

67 6- PDF

Matrix formulae and skein relations for cluster algebras from surfaces

- Gregg Musiker, L. Williams
- Mathematics
- 17 August 2011

This paper concerns cluster algebras with principal coefficients A(S,M) associated to bordered surfaces (S,M), and is a companion to a concurrent work of the authors with Schiffler [MSW2]. Given any… Expand

39 4- PDF

Higher cluster categories and QFT dualities

- S. Franco, Gregg Musiker
- Physics, Mathematics
- 3 November 2017

We present a unified mathematical framework that elegantly describes minimally SUSY gauge theories in even dimension, ranging from $6d$ to $0d$, and their dualities. This approach combines recent… Expand

11 4- PDF

Aztec Castles and the dP3 Quiver

- Megan Leoni, Gregg Musiker, Seth Neel, P. Turner
- Mathematics
- 19 August 2013

Bipartite, periodic, planar graphs known as brane tilings can be associated to a large class of quivers. This paper will explore new algebraic properties of the well-studied del Pezzo 3 quiver and… Expand

18 2- PDF

A COMPENDIUM ON THE CLUSTER ALGEBRA AND QUIVER PACKAGE IN Sage

- Gregg Musiker, C. Stump
- Mathematics
- 23 February 2011

This is the compendium of the cluster algebra and quiver package for Sage. The purpose of this package is to provide a platform to work with cluster algebras in graduate courses and to further… Expand

22 2- PDF

Combinatorial Interpretations for Rank-Two Cluster Algebras of Affine Type

- Gregg Musiker, J. Propp
- Mathematics, Computer Science
- Electron. J. Comb.
- 19 February 2006

TLDR

39 1- PDF

Gale-Robinson Sequences and Brane Tilings

- Sicong Zhang, Gregg Musiker, In-Jee Jeong
- Mathematics
- 2013

We study variants of Gale-Robinson sequences, as motivated by cluster algebras with principal coefficients. For such cases, we give combinatorial interpretations of cluster variables using brane… Expand

17 1- PDF