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 …

The 4-simplex equation is a higher-dimensional analogue of Zamolodchikov's tetrahedron
equation and the Yang–Baxter equation which are two of the most fundamental equations of …

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 …

It is known that the local Yang–Baxter equation is a generator of potential solutions to
Zamolodchikov's tetrahedron equation. In this paper, we show under which additional …

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 …

In this paper, we construct Yang–Baxter (YB) maps using Darboux matrices which are
invariant under the action of finite reduction groups. We present six-dimensional YB maps …

We study tetrahedron maps, which are set-theoretical solutions to the Zamolodchikov
tetrahedron equation, and their matrix Lax representations defined by the local Yang–Baxter …

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 present several algebraic and differential-geometric constructions of tetrahedron maps,
which are set-theoretical solutions to the Zamolodchikov tetrahedron equation. In particular …