Pablo Spiga: The Erdős-Ko-Rado theorem for permutation groups

Povzetek. The Erdős-Ko-Rado theorem determines the cardinality and describes the structure of a set of maximal cardinality of intersecting k-subsets from {1, …, n}. The theorem says that provided that n > 2k, a set of maximal cardinality of intersecting k-subsets from {1, …, n} has cardinality {n - 1 \choose k - 1} and is the set of all k-subsets that contain a common fixed element. Analogous results hold for many other objects other than sets, and in this talk we are concerned with an extension of the Erdős-Ko-Rado theorem to permutation groups.