Combinatória e Teoria dos Números

           Václav Linek, University of Winnipeg

    Sexta-feira, 26 de abril, sala IC2-96, 18:00hs 


                         Abstract

A generalized Skolem sequence is a sequence of positive
integers and null symbols (also called holes) with the following two
properties: (1) an integer j appears exactly twice in the sequence or
not at all, and (2) if j does appear in the sequence then exactly j-1
symbols separate the two appearences of j. For example, 2423543115,
31135242_54 and 3_232411_4 are all generalized Skolem sequences, where
"_"is the null symbol.

In this talk we give an overview of problems and results concerning
generalized Skolem sequences, and some of the techniques used to
construct them, as well as examples of how generalized Skolem
sequences are used to construct Steiner Triple Systems with prescribed
automorphism groups. Finally, we will discuss generalizations of the
idea of a generalized Skolem sequence!