A374820 Boolean-Chain Quilt Numbers: Square table of the number of ASM quilts of type B_n X C_k read down antidiagonals, where B_n is the Boolean lattice on an n-set and C_k is a chain of length k with k+1 elements.

1, 2, 4, 3, 4, 18, 4, 17, 199, 166, 5, 46, 199, 47000, 7579, 6, 100, 3252, 3813042, 410131245, 7828352

Offset: 1

Author

Sara Billey and Matjaz Konvalinka, Jul 21 2024

Keywords

• nonn
• tabl
• more

Comments

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

For k=2, these numbers are Antichain-Boolean numbers, see A374821.

These numbers are given by a polynomial in k for fixed n when k>=n.

Examples

			Square array begins:
        1,         2,       3,    4,   5,  6, ...
        4,         4,      17,   46, 100, ...
       18,       199,     199, 3252, ...
      166,     47000, 3813042, ...
     7579, 410131245, ...
  7828352, ...
		

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. A374819, A374821, A374822, A297622, A374824.