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Symmetric Permutations Avoiding Two Patterns
David Lonoff1 and Jonah Ostroff2
1Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104, USA
2Department of Mathematics, Brandeis University, Waltham, MA 02453, USA
Annals of Combinatorics 14 (1) pp.143-158 Springer, 2010
AMS Subject Classification: 05A05, 05A15; 05A19
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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