Pattern avoidance by even permutations

Andrew M. Baxter, Aaron D. Jaggard

Published 2011-06-18Version 1

We study questions of even-Wilf-equivalence, the analogue of Wilf-equivalence when attention is restricted to pattern avoidance by permutations in the alternating group. Although some Wilf-equivalence results break when considering even-Wilf-equivalence analogues, we prove that other Wilf-equivalence results continue to hold in the even-Wilf-equivalence setting. In particular, we prove that t(t-1)...321 and (t-1)(t-2)...21t are even-shape-Wilf-equivalent for odd t, paralleling a result (which held for all t) of Backelin, West, and Xin for shape-Wilf-equivalence. This allows us to classify the patterns of length 4, and to partially classify patterns of length 5 and 6. As with transition to involution-Wilf-equivalence, some (but not all) of the classical Wilf-equivalence results are preserved when we make the transition to even-Wilf-equivalence.