On the base size for the symmetric group acting on subsets

Zoltán Halasi
2012 Studia scientiarum mathematicarum Hungarica (Print)  
Let k, n be natural numbers with k ≤ n/2 and let X n,k denote the set of k-element subsets of {1, 2, . . . , n}. The symmetric group Sn acts in a natural way on the set X n,k . Motivated by the question of Robert Guralnick, we investigate the size of a minimal base for this action. We give constructions providing a minimal base if n = 2k or if n ≥ k 2 . We also describe a general process providing a base of size at most c times bigger than the size of a minimal base for some universal constant c.
more » ... universal constant c.
doi:10.1556/sscmath.49.2012.4.1222 fatcat:77l2dewgibhi3emxytz57pg5va