cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A374824 Boolean-Boolean Quilt Numbers: Triangular array T(n,k) of the number of ASM quilts of type B_n X B_k, where B_n is the Boolean lattice of subsets of an n-set ordered by inclusion.

Original entry on oeis.org

1, 4, 16, 18, 2309, 2406862, 166, 4001278
Offset: 1

Views

Author

Sara Billey and Matjaz Konvalinka, Jul 21 2024

Keywords

Comments

For k=1, these numbers are the Dedekind numbers given in A007153.

Examples

			Triangle begins:
    1;
    4,      16;
   18,    2309, 2406862;
  166, 4001278,     ..., ...;
  ...
		

Crossrefs

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.

Original entry on oeis.org

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

Views

Author

Sara Billey and Matjaz Konvalinka, Jul 25 2024

Keywords

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;
  ...
		

Crossrefs

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.

Original entry on oeis.org

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

Views

Author

Sara Billey and Matjaz Konvalinka, Jul 21 2024

Keywords

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, ...
		

Crossrefs

A374821 Antichain-Boolean Quilt Numbers: Square table of the number of ASM quilts of type B_n x A_2(j) read down antidiagonals, where B_n is the Boolean lattice and A_2(j) is the rank 2 poset with a unique minimal and maximal element and j atoms.

Original entry on oeis.org

2, 4, 4, 8, 16, 199, 16, 64, 2309, 47000, 32, 256, 28225, 4001278, 410131245, 64, 1024, 364217, 384285926
Offset: 1

Views

Author

Sara Billey and Matjaz Konvalinka, Jul 21 2024

Keywords

Crossrefs

Showing 1-4 of 4 results.