A335926 Number of distinct odd diagrams of permutations of n.

1, 2, 5, 17, 70, 351, 2041, 13732, 103873, 882213

Offset

1,2

Comments

The odd diagram of a permutation w of n is {(i,j) : j<w(i), i<w^{-1}(j) and w^{-1}(j)-i=1 (mod 2)}. Its cardinality is known as the odd length or number of odd inversions of w.

Links

Table of n, a(n) for n=1..10.

F. Brenti and A. Carnevale, Odd length: odd diagrams and descent classes, arXiv:1707.00987v2 [math.CO], 2020.

Francesco Brenti, Angela Carnevale, and Bridget Eileen Tenner, Odd diagrams, Bruhat order, and pattern avoidance, arXiv:2009.08865 [math.CO], 2020. Mentions this sequence.

Crossrefs

Cf. A289511.

Sequence in context: A263682 A049774 A317132 * A139402 A143382 A057219

Adjacent sequences: A335923 A335924 A335925 * A335927 A335928 A335929

Keyword

nonn,more

Author

Angela Carnevale, Jun 30 2020

Status

approved