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A365643
Number of permutations whose reverse-complement shares the same recording tableau in the Robinson-Schensted correspondence.
0
1, 1, 2, 2, 12, 24, 136, 344, 2872, 7108, 80672, 211056, 3032376
OFFSET
0,3
COMMENTS
This is an open problem from Martin's "Algebraic Combinatorics" lecture.
LINKS
Tucker J. Ervin, Blake Jackson, Jay Lane, Kyungyong Lee, Son Dang Nguyen, Jack O'Donohue, and Michael Vaughan, Permutations whose reverse shares the same recording tableau in the RS correspondence, Sém. Lothar. Combin. 86 (2022), Art. B86a, 15 pp.
Jeremy L. Martin, Lecture Notes on Algebraic Combinatorics, 2010-2023.
PROG
(SageMath)
def a(n): return sum(StandardTableaux(T.shape()).cardinality()
for T in StandardTableaux(n) if T == T.evacuation())
print([a(n) for n in range(13)])
CROSSREFS
Cf. A059304.
Sequence in context: A164961 A362192 A122007 * A137782 A131384 A052612
KEYWORD
nonn,more
AUTHOR
Dang-Son Nguyen, Sep 14 2023
STATUS
approved