A349456 Number of singular positroid varieties corresponding to derangements in S_n.

0, 0, 0, 0, 4, 30, 225, 1736, 14476, 132396

Offset: 0

Author

Jordan Weaver, Nov 16 2021

Keywords

• nonn
• more

Comments

a(n) is also the number of derangements whose chordal diagrams have crossed alignments.

a(n) counts the complement of A349413 in the set of all derangements of S_n (A000166).

Examples

			For n=4 the a(4)=4 derangements in one-line notation corresponding to singular positroid varieties are 2413, 3421, 3142, and 4312.
		

Links

• Sara C. Billey and Jordan E. Weaver, Criteria for smoothness of Positroid varieties via pattern avoidance, Johnson graphs, and spirographs, arXiv:2207.06508 [math.CO], 2022.
• S. Corteel, Crossings and alignments of permutations, arXiv:math/0601469 [math.CO], 2006.
• A. Knutson, T. Lam and D. Speyer, Positroid varieties: juggling and geometry, Compos. Math. 149 (2013), no. 10, 1710-1752.
• A. Postnikov, Total positivity, Grassmannians, and networks, arXiv:math/0609764 [math.CO], 2006.

Crossrefs

Cf. A000166, A349413, A349457, A349458.

Formula

a(n) = A000166(n) - A349413(n).