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We investigate pattern avoidance in alternating permutations andgeneralizations thereof. First, we study pattern avoidance in an alternatinganalogue of Young diagrams. In particular, we extend Babson-West's notion ofshape-Wilf equivalence to apply to alternating permutations and so generalizeresults of Backelin-West-Xin and Ouchterlony to alternating permutations.Second, we study pattern avoidance in the more general context of permutationswith restricted ascents and descents. We consider a question of Lewis regardingpermutations that are the reading words of thickened staircase Young tableaux,that is, permutations that have (k - 1) ascents followed by a descent, followedby (k - 1) ascents, et cetera. We determine the relative sizes of the sets ofpattern-avoiding (k - 1)-ascent permutations in terms of the forbidden pattern.Furthermore, we give inequalities in the sizes of sets of pattern-avoidingpermutations in this context that arise from further extensions ofshape-equivalence type enumerations.

Beyond alternating permutations: Pattern avoidance in Young diagrams and tableaux