Abstract: In the present paper we study general properties of good sequences by means
of a powerful and beautiful tool of combinatorics - the method of bijective proofs. A
good sequence is a sequence of positive integers k=1,2,... such that the element k occurs
before the last occurrence of k+1. We construct two bijections between the set of good
sequences of fixed length and the set of permutations of the same length. This allows us
to count good sequences as well as to calculate generating functions of statistics on good
sequences. We study avoiding patterns on good sequences and discuss their relation with
Eulerian polynomials. Finally, we describe particular interesting properties of
permutations, again using bijections.