Mathematics and Statistics
Restricted permutation, Pattern-avoiding permutation, Forbidden subsequence, Schröder number, Signed permutation, Generating tree
Gire, West, and Kremer have found ten classes of restricted permutations counted by the large Schröder numbers, no two of which are trivially Wilf-equivalent. In this paper we enumerate eleven classes of restricted signed permutations counted by the large Schröder numbers, no two of which are trivially Wilf-equivalent. We obtain five of these enumerations by elementary methods, five by displaying isomorphisms with the classical Schröder generating tree, and one by giving an isomorphism with a new Schröder generating tree. When combined with a result of Egge and a computer search, this completes the classification of restricted signed permutations counted by the large Schröder numbers in which the set of restrictions consists of two patterns of length 2 and two of length 3.
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Egge, E. S. (2006). Restricted Signed Permutations Counted by the Schröder Numbers. Discrete Mathematics, 306 (6), 552-563. Available at: https://doi.org/10.1016/j.disc.2006.01.013. Accessed via Faculty Work. Mathematics. Carleton Digital Commons. https://digitalcommons.carleton.edu/math_faculty/1
The definitive version is available at https://doi.org/10.1016/j.disc.2006.01.013