We investigate pattern avoidance in alternating permutations and generalizations thereof. First, we study pattern avoidance in an alternating analogue of Young diagrams. In particular, we extend Babson-West's notion of shape-Wilf equivalence to apply to alternating permutations and so generalize results of Backelin-West-Xin and Ouchterlony to alternating permutations. Second, we study pattern avoidance in the more general context of permutations with restricted ascents and descents. We consider a question of Lewis regarding permutations that are the reading words of thickened staircase Young tableaux, that is, permutations that have $k-1$ ascents followed by a descent, followed by $k-1$ ascents, et cetera. We determine the relative sizes of the sets of pattern-avoiding $(k-1)$-ascent permutations in terms of the forbidden pattern. Furthermore, inequalities in the sizes of sets of pattern-avoiding permutations in this context arise from further extensions of shape-equivalence type enumerations. This paper is the first of a two-paper series presenting the work of Beyond alternating permutations: Pattern avoidance in Young diagrams and tableaux (arXiv:1301.6796v1). The second in the series is Ascent-descent Young diagrams and pattern avoidance in alternating permutations (by the second author, submitted).
@article{10_37236_3246,
author = {Nihal Gowravaram and Ravi Jagadeesan},
title = {Beyond alternating permutations: pattern avoidance in {Young} diagrams and tableaux},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {4},
doi = {10.37236/3246},
zbl = {1300.05319},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3246/}
}
TY - JOUR
AU - Nihal Gowravaram
AU - Ravi Jagadeesan
TI - Beyond alternating permutations: pattern avoidance in Young diagrams and tableaux
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/3246/
DO - 10.37236/3246
ID - 10_37236_3246
ER -
%0 Journal Article
%A Nihal Gowravaram
%A Ravi Jagadeesan
%T Beyond alternating permutations: pattern avoidance in Young diagrams and tableaux
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/3246/
%R 10.37236/3246
%F 10_37236_3246
Nihal Gowravaram; Ravi Jagadeesan. Beyond alternating permutations: pattern avoidance in Young diagrams and tableaux. The electronic journal of combinatorics, Tome 20 (2013) no. 4. doi: 10.37236/3246
