A384529 Number of inequivalent sets S (cubic acute n-set), with cardinality A089676(n) >= 3, of points in {0,1}^n in real n-dimensional Euclidean space such that every angle determined by three distinct points in S is acute.

0, 0, 2, 5, 18, 3, 64

Offset: 1

Author

Dmitry I. Ignatov, Jun 01 2025

Keywords

• nonn
• hard
• more

Comments

Consider the 2^n points {0,1}^n in real Euclidean space. Then A089676(n) = maximal size of a subset S of these 2^n points such that there is no triple of points P, Q, R in S which subtends a right angle. That is, we are not allowed to have P-Q perpendicular to R-Q. Here we count such inequivalent sets of points under permutation of their coordinates.

Links

• D. Bevan, Sets of Points Determining Only Acute Angles and Some Related Coloring Problems, Electronic J. of Combinatorics, 13(1), 2006, #R12.

Crossrefs

Cf. A089676 (maximal set sizes), A289972 (labeled case).