Permutation Capacities and Oriented Infinite Paths

The notion of permutation capacities is motivated by and shows similarities with the Shannon capacity of graphs and its generalization to directed graphs called Sperner capacity. We show that families of oriented paths have a different behaviour with respect to these capacities than Shannon and Sperner capacities and their generalization to graph families do. The talk is based on the paper [Brightwell, G., G. Cohen, E. Fachini, M. Fairthorne, J. Körner, G. Simonyi, and Á. Tóth, Permutation capacities of families of oriented infinite paths, SIAM J. Discrete Math. 24 (2010), 441-456].