This first introductory text to discrete integrable systems introduces key notions of
integrability from the vantage point of discrete systems, also making connections with the …

We introduce a class of integrable dynamical systems of interacting classical matrix-valued
fields propagating on a discrete space-time lattice, realized as many-body circuits built from …

Connections between set-theoretic Yang–Baxter and reflection equations and quantum
integrable systems are investigated. We show that set-theoretic R-matrices are expressed as …

A relationship between the tetrahedron equation for maps and the consistency property of
integrable discrete equations on Z 3 is investigated. Our approach is a generalization of a …

In the recent years there is a growing interest in deriving and extending discrete integrable
systems to the non-abelian domain. At the same time there is an intrinsic connection of …

We consider involutive, non-degenerate, finite set-theoretic solutions of the Yang–Baxter
equation (YBE). Such solutions can be always obtained using certain algebraic structures …

We examine links between the theory of braces and set-theoretical solutions of the Yang–
Baxter equation, and fundamental concepts from the theory of quantum integrable systems …

We construct birational maps that satisfy the parametric set-theoretical Yang–Baxter
equation and its entwining generalisation. For this purpose, we employ Darboux …

We present the explicit form of a family of Liouville integrable maps in 3 variables, the so-
called triad family of maps and we propose a multi-field generalisation of the latter. We show …

We show that integrable involutive maps, due to the fact they admit three integrals in
separated form, can give rise to equations, which are consistent around the cube and which …