  We define a class L_{n, k} of permutations that generalizes alternating
(up-down) permutations and give bijective proofs of certain pattern-avoidance
results for this class. As a special case of our results, we give two
bijections between the set A_{2n}(1234) of alternating permutations of length
2n with no four-term increasing subsequence and standard Young tableaux of
shape (3^n), and between the set A_{2n + 1}(1234) and standard Young tableaux
of shape (3^{n - 1}, 2, 1). This represents the first enumeration of
alternating permutations avoiding a pattern of length four. We also extend
previous work on doubly-alternating permutations (alternating permutations
whose inverses are alternating) to our more general context.
  The set L_{n, k} may be viewed as the set of reading words of the standard
Young tableaux of a certain skew shape. In the last section of the paper, we
expand our study to consider pattern avoidance in the reading words of standard
Young tableaux of any skew shape. We show bijectively that the number of
standard Young tableaux of shape lambda/mu whose reading words avoid 213 is a
natural mu-analogue of the Catalan numbers (and in particular does not depend
on lambda, up to a simple technical condition), and that there are similar
results for the patterns 132, 231 and 312.
