78 citations · 237 across the 20 of their papers we have counts for
22 papers
Full symmetric Toda system: QR-solution for complete DLNT-family
Yury B. Chernyakov, Georgy I. Sharygin, Dmitry V. Talalaev
The paper is devoted to the algebraic and geometric aspects of the full symmetric Toda system. We construct a solution to the complete Deift-Li-Nanda-Tomei flows system using the Q…
Extensions of Yang-Baxter sets
Valeriy G. Bardakov, Dmitry V. Talalaev
The paper extends the notion of braided set and its close relative - the Yang-Baxter set - to the category of vector spaces and explore structure aspects of such a notion as morphi…
Vertex electrical model: lagrangian and non-negative properties
Dmitry Talalaev
This note is a modest addition to the work arXiv:2109.13952. Here we construct an embedding of the space of electrical networks to the totally non-negative Lagrangian Grassmannian…
Electrical Networks, Lagrangian Grassmannians and Symplectic Groups
Boris Bychkov, Vassily Gorbounov, Anton Kazakov +1
We refine the result of T. Lam \cite{L} on embedding the space of electrical networks on a planar graph with boundary points into the totally non-negative Grassmannian $\…
Functional Relations on Anisotropic Potts Models: from Biggs Formula to the Tetrahedron Equation
Boris Bychkov, Anton Kazakov, Dmitry Talalaev
We explore several types of functional relations on the family of multivariate Tutte polynomials: the Biggs formula and the star-triangle () transformation at the critical poi…
Electrical varieties as vertex integrable statistical models
Vassily Gorbounov, Dmitry Talalaev
We propose a new approach to studying electrical networks interpreting the Ohm law as the operator which solves certain Local Yang-Baxter equation. Using this operator and the medi…