Combinatorics on permutation tableaux of type A and type B

Authors:
Sylvie Corteel;Jang Soo Kim
Affiliations:
LIAFA, CNRS et Université Paris-Diderot 7, Case 7014, 75205 Paris Cedex 13, France;School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA
Venue:
European Journal of Combinatorics
Year:
2011

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Abstract

We give two bijective proofs of a result of Corteel and Nadeau. We find a generating function related to unrestricted columns of permutation tableaux. As a consequence, we obtain a sign-imbalance formula for permutation tableaux. We extend the first bijection of Corteel and Nadeau between permutations and permutation tableaux to type B objects. Using this type B bijection, we generalize a result of Lam and Williams. We prove that the bijection of Corteel and Nadeau and our type B bijection can be expressed as zigzag maps on the alternative representation.