Leírás
Abstract:
Let G be a finite permutation group acting on a set X. A base for G is a subset of X such that its pointwise stabilizer is the identity. A base is called minimal if no proper subset of it is a base. An irredundant base of G is a sequence of points of X such that the pointwise stabilizer of all the points is the identity and no point is fixed by the stabilizer of its predecessors.
During this talk, we study the structure of two subsets of the natural numbers associated with the action of G on X. In particular, we consider the sets of cardinalities of all the minimal and irredundant bases of G, respectively. For example, it is proved that the set of cardinalities of the irredundant base is an interval of natural numbers. Moreover, given a set Y of natural numbers, we give some conditions on Y that ensure the existence of both intransitive and transitive groups G having Y as the set of cardinalities of minimal or irredundant bases.
Based on a joint work with Francesca Dalla Volta and Pablo Spiga.
Az előadást Zoom-on is közvetítjük:
https://us06web.zoom.us/j/83223024232?pwd=MJEovn9QoQlxnTRvSoHYbEvN2NhZzR.1
Meeting ID: 832 2302 4232
Passcode: 482129