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Symmetric Permutations Avoiding Two Patterns
David Lonoff1 and Jonah Ostroff2
1Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104, USA
lonoff@math.upenn.edu
2Department of Mathematics, Brandeis University, Waltham, MA 02453, USA
jostroff@brandeis.edu
Annals of Combinatorics 14 (1) pp.143-158 Springer, 2010
AMS Subject Classification: 05A05, 05A15; 05A19
Abstract:
Symmetric pattern-avoiding permutations are restricted permutations which are invariant under actions of certain subgroups of D4, the symmetry group of a square. We examine pattern-avoiding permutations with 1800 rotational-symmetry. In particular, we use combinatorial techniques to enumerate symmetric permutations which avoid one pattern of length three and one pattern of length four. Our results involve well-known sequences such as the alternating Fibonacci numbers, triangular numbers, and powers of two.
Keywords: Fibonacci identity, pattern-avoiding permutation, restricted permutation, signed permutation, symmetric permutation

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