11 citations · 37 across the 11 of their papers we have counts for
13 papers
Snake graphs and their characteristic polynomials
James P. Bradshaw, Philipp Lampe, Dusan Ziga
The aim of the article is to understand the combinatorics of snake graphs by means of linear algebra. In particular, we apply Kasteleyn's and Temperley--Fisher's ideas about spectr…
Exchange graphs for mutation-finite non-integer quivers of rank 3
Anna Felikson, Philipp Lampe
Skew-symmetric non-integer matrices with real entries can be viewed as quivers with non-integer weights of arrows. One can mutate such quivers according to usual rules of quiver mu…
Cluster algebras and discrete integrability
Andrew N. W. Hone, Philipp Lampe, Theodoros E. Kouloukas
Cluster algebras are a class of commutative algebras whose generators are defined by a recursive process called mutation. We give a brief introduction to cluster algebras, and expl…
An expansion formula for type A and Kronecker quantum cluster algebras
Ilke Canakci, Philipp Lampe
We introduce an expansion formula for elements in quantum cluster algebras associated to type A and Kronecker quivers with principal quantization. Our formula is parametrized by pe…
Factoriality and class groups of cluster algebras
Ana Garcia Elsener, Philipp Lampe, Daniel Smertnig
Locally acyclic cluster algebras are Krull domains. Hence their factorization theory is determined by their (divisor) class group and the set of classes containing height-1 prime i…
Variations on Baur--Marsh's determinant
Philipp Lampe
Baur and Marsh computed the determinant of a matrix assembled from the cluster variables in a cluster algebra of type A. In this article we wish to describe two variations. On the…