We use the consistency approach to classify discrete integrable three-dimensional
equations of the octahedron type. They are naturally treated on the root lattice Q (A 3) and …

We show that the Wynn recurrence (the missing identity of Frobenius of the Padé
approximation theory) can be incorporated into the theory of integrable systems as a …

We present new solutions of the functional Zamolodchikov tetrahedron equation in terms of
birational maps in totally non-commutative variables. All the maps originate from Desargues …

We introduce and solve the non-commutative version of the Hermite–Padé type I
approximation problem. Its solution, expressed by quasideterminants, leads in a natural way …

We show that solution to the Hermite–Padé type I approximation problem leads in a natural
way to a subclass of solutions of the Hirota (discrete Kadomtsev–Petviashvili) system and of …

We review recent results on the connection between the Hermite–Padé approximation
problem, multiple orthogonal polynomials, and multidimensional Toda equations in …

We introduce integrable multicomponent non-commutative lattice systems, which can be
considered as analogues of the modified Gel'fand–Dikii hierarchy. We present the …

We study the interpolation analogue of the Hermite–Padé type I approximation problem. We
provide its determinant solution and we write down the corresponding integrable discrete …

We show that the discrete Kadomtsev–Petviashvili (KP) equation with sources obtained
recently by the “source generalization” method can be incorporated into the squared …

D is an arbitrary division ring (skew field), associated with the Veblen configuration, and we
show that such a map provides solutions to the functional dynamical pentagon equation. We …