Title: Modified Snake Graph : Type B and C
Abstract: Fomin and Zelevinsky demonstrated that θ-invariant triangulations of P_{2n+2} correspond bijectively to the clusters of cluster algebras of type B_n or C_n. Additionally, cluster variables are associated with the orbits of the θ-action on the diagonals of P_{2n+2}. In this talk, I will present how to describe the cluster variables of type B_n and C_n with principal coefficients using the perfect matchings of modified snake graphs.