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math.CO2013★ 1 cited
Laurent Phenomenon Sequences
Joshua Alman, Cesar Cuenca, Jiaoyang Huang
In this paper, we undertake a systematic study of recurrences x_{m+n}x_{m} = P(x_{m+1}, ..., x_{m+n-1}) which exhibit the Laurent phenomenon. Some of the most famous among these se…
math.CO2013★ 2 cited
Circular Planar Electrical Networks II: Positivity Phenomena
Joshua Alman, Carl Lian, Brandon Tran
Curtis-Ingerman-Morrow characterize response matrices for circular planar electrical networks as symmetric square matrices with row sums zero and non-negative circular minors. In t…
math.CO2013★ 6 cited
Circular Planar Electrical Networks I: The Electrical Poset EP_{n}
Joshua Alman, Carl Lian, Brandon Tran
Following de Verdière-Gitler-Vertigan and Curtis-Ingerman-Morrow, we prove a host of new results on circular planar electrical networks. We introduce a poset EP_{n} of electrical n…