A374819 Triangle read by rows: T(n,k) is the number of functions on the Boolean lattice B_n satisfying f({}) =0, f([n])=k, and the Boolean growth rule: f(J union {i})-f(J) in {0,1} for all subsets J of [n]={1, ..., n} and all i in [n]\J, 0 <= k <= n.

1, 1, 1, 1, 4, 1, 1, 18, 18, 1, 1, 166, 656, 166, 1, 1, 7579, 189967, 189967, 7579, 1, 1, 7828352

Offset: 0

Author

Sara Billey and Matjaz Konvalinka, Jul 25 2024

Keywords

• nonn
• tabl
• more

Comments

For k=1, these numbers are the Dedekind numbers A007153 counting the number of monotone Boolean functions or equivalently antichains of subsets of an n-set containing at least one nonempty set.

Examples

			Triangle begins:
  1;
  1,    1;
  1,    4,      1;
  1,   18,     18,      1;
  1,  166,    656,    166,    1;
  1, 7579, 189967, 189967, 7579, 1;
  ...
		

Links

• Sara Billey and Matjaž Konvalinka, Generalized rank functions and quilts of alternating sign matrices, arXiv:2412.03236 [math.CO], 2024. See p. 32.

Crossrefs

Cf. A000372, A007153, A374820, A374821, A374822, A297622, A374824.