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

0,3

Comments

The number of distinct hyperplanes is given by A381243.

Links

Table of n, a(n) for n=0..4.

Prog

(SageMath) 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()

Crossrefs

Cf. A019589, A175176, A362968, A381243.

Sequence in context: A003042 A000887 A118542 * A007155 A265092 A262032

Adjacent sequences: A381241 A381242 A381243 * A381245 A381246 A381247

Keyword

nonn,more,hard

Author

Max Alekseyev, Feb 17 2025

Status

approved