A381244 Number of regions in the arrangement of hyperplanes corresponding to the nonzero differences of two permutations of order n.

1, 1, 2, 12, 3696

Offset: 0

Author

Max Alekseyev, Feb 17 2025

Keywords

• nonn
• more
• hard

Comments

The number of distinct hyperplanes is given by A381243.

Crossrefs

Cf. A019589, A175176, A362968, A381243.

Programs

Sage

def a381244(n): return HyperplaneArrangements(QQ,tuple(f'x{i}' for i in range(n)))([[list(r),0] for p in Permutations(n) for r in Permutations([p[i]-i-1 for i in range(n)]) if vector(r)>0]).n_regions()