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math.CO2022★ 4 cited
Electrical networks and the Grove algebra
Yibo Gao, Thomas Lam, Zixuan Xu
We study the ring of regular functions on the space of planar electrical networks, which we coin the grove algebra. This algebra is an electrical analogue of the Plücker ring studi…
math.CO2020★ 2 cited
Dihedral Sieving on Cluster Complexes
Zachary Stier, Julian Wellman, Zixuan Xu
The cyclic sieving phenomenon of Reiner, Stanton, and White characterizes the stabilizers of cyclic group actions on finite sets using q-analogue polynomials. Eu and Fu demonstrate…
math.CO2019
Extended Nestohedra and their Face Numbers
Quang Dao, Christina Meng, Julian Wellman +3
Nestohedra are a family of convex polytopes that includes permutohedra, associahedra, and graph associahedra. In this paper, we study an extension of such polytopes, called extende…