  This thesis deals with three different aspects of the combinatorics of
permutations. In the first two papers, two flavours of pattern avoiding
permutations are examined; and in the third paper Young tableaux, which are
closely related to permutations via representation theory, are studied.
  In the first paper we give solutations to several interesting problems
regarding pattern avoiding doubly alternating permutations, such as finding a
bijection between 1234-avoiding permutations and 1234-avoiding doubly
alternating permutations of twice the size.
  In the second paper partial permutations which can be extended to pattern
avoiding permutations are examined. A general algorithm is presented which is
subsequently used to solve many different problems.
  The third paper deals with involutions on Young tableaux. There is a
surprisingly large collection of relations among these involutions and in the
paper we make the effort to study them systematically in order to create a
coherent theory. The most interesting result is that for Littlewood-Richardson
tableaux, $a^3=1$, wher5e $a$ is the composition of three different
involutions: the fundamental symmetry map, the reversal and rotation
involutions.
