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%I #30 Dec 29 2023 16:42:56
%S 1,1,2,2,12,24,136,344,2872,7108,80672,211056,3032376
%N Number of permutations whose reverse-complement shares the same recording tableau in the Robinson-Schensted correspondence.
%C This is an open problem from Martin's "Algebraic Combinatorics" lecture.
%H Tucker J. Ervin, Blake Jackson, Jay Lane, Kyungyong Lee, Son Dang Nguyen, Jack O'Donohue, and Michael Vaughan, <a href="https://www.mat.univie.ac.at/~slc/wpapers/s86jackson.html">Permutations whose reverse shares the same recording tableau in the RS correspondence</a>, Sém. Lothar. Combin. 86 (2022), Art. B86a, 15 pp.
%H Jeremy L. Martin, <a href="https://jlmartin.ku.edu/LectureNotes.pdf">Lecture Notes on Algebraic Combinatorics</a>, 2010-2023.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Robinson%E2%80%93Schensted_correspondence">Robinson-Schensted correspondence</a>.
%o (SageMath)
%o def a(n): return sum(StandardTableaux(T.shape()).cardinality()
%o for T in StandardTableaux(n) if T == T.evacuation())
%o print([a(n) for n in range(13)])
%Y Cf. A059304.
%K nonn,more
%O 0,3
%A _Dang-Son Nguyen_, Sep 14 2023