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Research in the Combinatorics

Research in the Combinatorics

Research in the Combinatorics axis mainly looks into enumerating combinatorial objects, discovering new bijections preserving some combinatorial statistics, the exhaustive and random generation of combinatorial structures and studying graphs and lattices properties. We focus on the behavior of patterns and statistics on subsets of words or on the symmetric group. We focus on showing bijectively or analytically the equidistribution/equipopularity of certain statistics, on enumerating or generating efficiently equivalence classes having a given distribution for a given pattern. Concerning graphs we want to bring to light various parameters of graphs coloring and to define constrained subgraphs of a given graph; and for lattices, we consider the lattices properties of ordered structures related to binary (labeled or unlabeled) trees as well as those of their subsets and non-associative concatenation related to the language theory.

The research work carried out under the Networking axis concerns service level, autonomy and mobility in different environments. Our research activities highlight our expertise in the field of networks and services with a mastery of the concept of Autonomic Computing and self-management for an end-to-end service level guarantee (Quality of Service (QoS), security and mobility) within wired, wireless and mobile environments deploying different QoS models. The Internet of Things (IoT), Mesh Networks, Cloud Computing and Networking as well as Wireless Sensor Networks (WSN), Vehicular Ad-hoc Network (VANET) and Service- Oriented Architectures (SOA) ) are concrete examples for the studies we are conducting to strengthen our expertise in the Networking field. In order to meet the users’ requirements in terms of service level guarantee for heterogeneous application flows conveyed in several kinds of networks (IoT, Mesh, Cloud, WSN, VANET), the expertise that we are developing in the Networking axis is raising important research challenges covering several application areas such as Smart Cities, E-health and Intelligent Transport Systems (ITS). In this context, we are interested in Quality of Service, Security, Privacy, Trust and Optimization of interactions and exchanges between communicating objects in these emerging environments.


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