A375346 Number of orientations of the uniform Lagrangian matroid on n elements.

1, 6, 38, 990, 395094, 33433683534

Offset: 1

Author

Jesse Selover, Aug 12 2024

Keywords

• nonn
• more

Comments

a(n) is the number of functions F from the powerset of {1, ..., n} to {-1, +1} with F(empty set) = +1 and satisfying the constraint: F({i} union S) != F({j} union S) => F(S) != F({i,j} union S) for any subset S and distinct i,j not in S.

Links

• Tobias Boege, Jesse Selover, and Maksym Zubkov, Sign patterns of principal minors of real symmetric matrices, arXiv:2407.17826 [math.CO], 2024-2025 (see also code and data). See Table 2 on p. 10.
• Richard F. Booth, Alexandre V. Borovik, Israel M. Gelfand, and Neil White, Oriented Lagrangian Matroids, European Journal of Combinatorics, 22(5) (2001), 639-656.

Crossrefs

Cf. A307334.

Formula

a(n) = (1/3) * A307334(n) for n >= 2. - Tobias Boege, Jan 22 2025

Extensions

a(6) from Tobias Boege, Jan 22 2025