V. D. Blondel Department of Mathematical Engineering University of Louvain Avenue Georges Lemaitre, 4 B-1348 Louvain-la-Neuve Belgium Email: [email protected] J. Cassaigne Institut de Mathématiques de Luminy UPR 9016 Campus de Luminy, Case 907 13288 Marseille Cedex 9 France Email: [email protected] J. Karhumäki Dept. of Math. & TUCS University of Turku FIN-20014 Turku Finland Email: ...

We prove the freeness conjecture of Broué, Malle and Rouquier for the Hecke algebras associated to most of the primitive complex 2-reflection groups with a single conjugacy class of reflections.

Using free simplicial groups, it is shown how to construct a free or totally free 2-crossed module on suitable construction data. 2-crossed complexes are introduced and similar freeness results for these are discussed.

We give natural examples of factors of the Muchnik lattice which capture intuitionistic propositional logic (IPC), arising from the concepts of lowness, 1-genericity, hyperimmune-freeness and computable traceability. This provides a purely computational semantics for IPC.

Using free simplicial groups, it is shown how to construct a free or totally free 2-crossed module on suitable construction data. 2-crossed complexes are introduced and similar freeness results for these are discussed.

We propose to validate experimentally a theory of software certification that proceeds from assessment of confidence in fault-freeness (due to standards) to conservative prediction of failure-free operation.

I consider the problem of allocating N indivisible objects among N agents according to their preferences when transfers are absent and an outside option may exist. I study the tradeo between fairness and e ciency in the class of strategy-proof mechanisms. The main nding is that for strategy-proof mechanisms the following e ciency and fairness criteria are mutually incompatible: (1) ex-post e ci...

In the distributed subgraph-freeness problem, we are given a graph H , and asked to determine whether the network graph contains H as a subgraph or not. Subgraph-freeness is an extremely local problem: if the network had no bandwidth constraints, we could detect any subgraph H in |H| rounds, by having each node of the network learn its entire |H|-neighborhood. However, when bandwidth is limited...

Cake cutting has been recognized as a fundamental model in fair division, and several envy-free cake cutting algorithms have been proposed. Recent works from the computer science field proposed novelmechanisms for cake cutting, whose approaches are based on the theory of mechanism design; these mechanisms are strategy-proof, i.e., no agent has any incentive to misrepresent her utility function,...

We deal with the problem of designing one-sided error property testers for cycle-freeness in bounded degree graphs. Such a property tester always accepts forests. Furthermore, when it rejects an input, it provides a short cycle as a certificate. The problem of testing cycle-freeness in this model was first considered by Goldreich and Ron [13]. They give a constant time tester with two-sided err...