A365643 Number of permutations whose reverse-complement shares the same recording tableau in the Robinson-Schensted correspondence.

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

Table of n, a(n) for n=0..12.

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.

Wikipedia, Robinson-Schensted correspondence.

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

Adjacent sequences: A365640 A365641 A365642 * A365644 A365645 A365646

Keyword

nonn,more

Author

Dang-Son Nguyen, Sep 14 2023

Status

approved