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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.
4
1, 2, 4, 3, 4, 18, 4, 17, 199, 166, 5, 46, 199, 47000, 7579, 6, 100, 3252, 3813042, 410131245, 7828352
OFFSET
1,2
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.
LINKS
Sara Billey and Matjaž Konvalinka, Generalized rank functions and quilts of alternating sign matrices, arXiv:2412.03236 [math.CO], 2024. See p. 32.
EXAMPLE
Square array begins:
1, 2, 3, 4, 5, 6, ...
4, 4, 17, 46, 100, ...
18, 199, 199, 3252, ...
166, 47000, 3813042, ...
7579, 410131245, ...
7828352, ...
CROSSREFS
KEYWORD
nonn,tabl,more
AUTHOR
STATUS
approved