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math.CO2023
On the correspondence between perfect matchings and compatible pairs for affine cluster algebra
Ivan Ip, Duy Phan
We study cluster algebra of affine type by using two methods including counting the numbers of perfect matchings on snake graphs and compatible pairs on maximal Dyck pa…
math.QA2023
On the polynomiality conjecture of cluster realization of quantum groups
Ivan Chi-Ho Ip, Jeff York Ye
In this paper, we give a sufficient and necessary condition for a regular element of a quantum cluster algebra to be universally polynomial. This resol…