… Several templates are studied in this thesis including the classical templates (polyhedra,
zonotopes and ellipsoids) but also more elaborate ones that provide a richer family of sets but …

… It is known that the shape and size of a zonotope are completely determined by … a zonotope
to describe its size here (the details on the weighted Frobenius norm based size of zonotope …

… Xk as a zonotope with the center cx,k and the shape matrix Rx,k such Xk = 〈cx,k,Rx,k〉,
the zonotopic state at the next time instant k + 1 defined as Xk+1 is bounded by a zonotope …

… However, from (1c), we know that it is easy to obtain a box to bound a zonotope ie we can
easily obtain the upper and lower bounds of the zonotope. Therefore, it is more efficient to use …

… The prediction step uses the state zonotope at the previous time instant, the zonotopes of …
to produce a prediction zonotope. In the update step, the prediction zonotope is combined with …

We describe the cone of deformations of a Coxeter permutahedron, or equivalently, the nef
cone of the toric variety associated to a Coxeter complex. This class of polytopes contains …

… Q]Bd, where the symbol ↓d (·) denotes the reduction of the order of a zonotope r to d, ˆHT is
… Thus, we propose to use the notion of interval hull of zonotopes here to obtain the interval of …

… In 2017, Deza, Manoussakis, and Onn [15] introduced a lower bound that is achieved by a
family of lattice zonotopes, referred to as primitive zonotopes. They proved that δ(d,k) ≥ ⌊(k +…

… Zonotopes are a special type of polytope which are combinatorially … We can define a zonotope
as the Minkowski sum of a set of … We can map each face F of a zonotope to an unique sign …

… zonotopes by Antoine Deza, Lionel Pournin, and Rado Rakotonarivo provides geometric and
combinatorial properties for primitive zonotopes… vertices of a primitive zonotope that can be …