Séminaire Lotharingien de Combinatoire, 93B.70 (2025), 12 pp.
Esther Banaian, Elise Catania, Christian Gaetz, Miranda Moore, Gregg Musiker and Kayla Wright
Twists, r-Dimer Covers, and Web Duality
Abstract.
We study a twisted version of Fraser-Lam-Le's higher boundary measurement map using face weights instead of edge weights, thereby providing Laurent monomial expansions, in Pl\"ucker coordinates, for twisted web immanants for Grassmannians. Combined with our computation that web immanants for Gr(3,12) and Gr(4,12) correspond to webs indexed by transposed standard Young tableaux, we recover and extend formulas of Elkin-Musiker-Wright for twists of certain cluster variables.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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