132-avoiding two-stack sortable permutations, Fibonacci numbers, and Pell numbers

Authors:
Eric S. Egge;Toufik Mansour
Affiliations:
Department of Mathematics, Gettysburg College, Gettysburg, PA;Department of Mathematics, Haifa University, 31905 Haifa, Israel
Venue:
Discrete Applied Mathematics
Year:
2004

Citing 12
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Abstract

We describe the recursive structures of the set of two-stack sortable permutations which avoid 132 and the set of two-stack sortable permutations which contain 132 exactly once. Using these results and standard generating function techniques, we enumerate two-stack sortable permutations which avoid (or contain exactly once) 132 and which avoid (or contain exactly once) an arbitrary permutation τ. In most cases the number of such permutations is given by a simple formula involving Fibonacci or Pell numbers.