A396320 Number of inequivalent strict ternary closure operators on a set of n elements.

1, 1, 3, 14, 165, 14296, 87602831

Offset

0,3

Comments

A closure operator cl on a set X is strict if the empty set is closed; it is n-ary if for all subsets S of X, cl(A) being a subset of S for all subsets A of X with cardinality no more than n implies that S is closed.

a(n) is also the number of non-isomorphic ternary convexities on a set of n elements (see Kubiś).

Links

Table of n, a(n) for n=0..6.

Wiesław Kubiś, Separation properties of convexity spaces, Journal of Geometry 74 (2002), pp. 110-119.

Tian Vlasic, Python Program

Wikipedia, Closure operator.

Formula

a(n) <= A108798(n).

Example

The a(3)=14 inequivalent systems are ({} and {1,2,3} not shown):
  {1,2}
  {1}
  {1},{2}
  {1},{1,2}
  {1,2},{2,3}
  {1},{2},{1,2}
  {1,2},{1,3}
  {1},{2},{3}
  {1},{1,2},{1,3}
  {1},{1,2},{2,3}
  {1},{2},{1,2},{1,3}
  {1},{2},{3},{1,2},{1,3}
  {1,2},{1,3},{2,3}
  {1},{2},{3},{1,2},{1,3},{2,3}

Crossrefs

Cf. A395658, A364656, A334255, A358144, A358152, A356544.

Cf. A108798.

Sequence in context: A090897 A120459 A272368 * A108798 A260995 A220438

Adjacent sequences: A396313 A396317 A396318 * A396321 A396322 A396323

Keyword

nonn,hard,more

Author

Tian Vlasic, May 21 2026

Extensions

a(6) from Robert P. P. McKone, May 23 2026

Status

approved