The practise of theoretical design has not traditionally been one of those areas of applied mathematics where well-posed questions lead directly to well-de ned answers. Instead, combinatorial arrangements are typically rst proposed as designs on more or less obscure and intuitive grounds; various precisely de ned notions of design optimality might be employed, but almost exclusively to con rm t...

We provide new combinatorial theorems on the structure of graphs that are contained as contractions in graphs of large treewidth. As a consequence of our combinatorial results we unify and significantly simplify contraction bidimensionality theory—the meta algorithmic framework to design efficient parameterized and approximation algorithms for contraction closed parameters.

The probability that the commutator of two group elements is equal to a given element has been introduced in literature few years ago. Several authors have investigated this notion with methods of the representation theory and with combinatorial techniques. Here we illustrate that a wider context may be considered and show some structural restrictions on the group.

In the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concurring the simplex algorithm. We describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes. 

Abstract From climate change to disruptive technologies, policymakers constantly face new problems calling for unprecedented institutional solutions. Yet, we still poorly understand the inventive process leading emergence of forms. Existing theories argue that exogenous changes provide incentives and opportunities invention. However, they fail explain how endogenously structures their emergence...