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Enumerating rc-Invariant Permutations with No Long Decreasing Subsequences
Eric S. Egge
Department of Mathematics, Carleton College, Northfield, MN 55057, USA
eegge@carleton.edu
Annals of Combinatorics 14 (1) pp.85-101 Springer, 2010
AMS Subject Classification: 05A05, 05A15, 05A19
Abstract:
We use the Robinson-Schensted-Knuth correspondence and Sch¨utzenberger's evacuation of standard tableaux to enumerate permutations and involutions which are invariant under the reverse-complement map and which have no decreasing subsequences of length k. These enumerations are in terms of numbers of permutations with no decreasing subsequences of length approximately k/2 ; we use known results concerning these quantities to give explicit formulas when k ≤ 6.
Keywords: domino tableaux, pattern-avoiding permutation, restricted permutation, reversecomplement map, Robinson-Schensted-Knuth correspondence, tableaux

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