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.

A361912 The number of unlabeled graded posets with n elements.

Original entry on oeis.org

1, 1, 2, 4, 10, 28, 93, 354, 1621, 9110, 64801, 595976, 7204091, 115561423, 2473540433, 70853213144, 2720354016419, 140170631441858, 9702605436760235, 903309202327818566, 113234129823368903523, 19137461395401601912043, 4366007821745938984134203
Offset: 0

Views

Author

Martin Rubey, Mar 29 2023

Keywords

Comments

A partially ordered set is graded if all maximal chains have the same length. This is called tiered by some authors.

Links

Crossrefs

Row sums of A361957.
Cf. A000112, A223911 (labeled), A001833, A361920, A361959 (connected).

Programs

  • PARI
    \\ See PARI link in A361957 for program code.
A361912seq(20) \\ Andrew Howroyd, Apr 03 2023
  • Sage
    sum(1 for P in posets(n) if P.is_graded())

Extensions

Terms a(8) and beyond from Andrew Howroyd, Mar 30 2023

A361956 Triangle read by rows: T(n,k) is the number of labeled tiered posets with n elements and height k.

Original entry on oeis.org

1, 0, 1, 0, 1, 2, 0, 1, 6, 6, 0, 1, 50, 36, 24, 0, 1, 510, 510, 240, 120, 0, 1, 7682, 10620, 4800, 1800, 720, 0, 1, 161406, 312606, 136920, 47040, 15120, 5040, 0, 1, 4747010, 13439076, 5630184, 1678320, 493920, 141120, 40320, 0, 1, 194342910, 821218110, 319384800, 83963880, 21137760, 5594400, 1451520, 362880
Offset: 0

Views

Author

Andrew Howroyd, Apr 02 2023

Keywords

Comments

A tiered poset is a partially ordered set in which every maximal chain has the same length.

Examples

			Triangle begins:
  1;
  0, 1;
  0, 1,      2;
  0, 1,      6,      6;
  0, 1,     50,     36,     24;
  0, 1,    510,    510,    240,   120;
  0, 1,   7682,  10620,   4800,  1800,   720;
  0, 1, 161406, 312606, 136920, 47040, 15120, 5040;
  ...

Links

Crossrefs

Row sums are A223911.
Column k=2 is A052332.
Main diagonal is A000142.
The unlabeled version is A361957.
Cf. A222864, A361951.

Programs

  • PARI
    S(M)={my(N=matrix(#M-1, #M-1, i, j, sum(k=1, i-j+1, (2^j-1)^k*M[i-j+1, k])/j!)); for(i=1, #N, for(j=1, i, N[i,j] -= sum(k=1, j-1, N[i-k, j-k]/k!))); N}
C(n)={my(M=matrix(n+1,n+1), R=M); M[1,1]=R[1,1]=1; for(h=1, n, M=S(M); for(i=h, n, R[i+1,h+1] = i!*vecsum(M[i-h+1,]))); R}
{ my(A=C(7)); for(i=1, #A, print(A[i, 1..i])) }

A361958 Triangle read by rows: T(n,k) is the number of connected unlabeled tiered posets with n elements and height k.

Original entry on oeis.org

1, 0, 1, 0, 2, 1, 0, 4, 3, 1, 0, 10, 10, 4, 1, 0, 27, 34, 16, 5, 1, 0, 88, 146, 66, 23, 6, 1, 0, 328, 739, 326, 106, 31, 7, 1, 0, 1460, 4671, 1932, 566, 156, 40, 8, 1, 0, 7799, 37088, 14104, 3577, 878, 217, 50, 9, 1, 0, 51196, 376524, 128652, 27563, 5740, 1276, 290, 61, 10, 1
Offset: 1

Views

Author

Andrew Howroyd, Apr 03 2023

Keywords

Comments

A tiered poset is a partially ordered set in which every maximal chain has the same length.

Examples

			Triangle begins:
  1;
  0,    1;
  0,    2,    1;
  0,    4,    3,    1;
  0,   10,   10,    4,   1;
  0,   27,   34,   16,   5,   1;
  0,   88,  146,   66,  23,   6,  1;
  0,  328,  739,  326, 106,  31,  7, 1;
  0, 1460, 4671, 1932, 566, 156, 40, 8, 1;
  ...

Links

Crossrefs

Row sums are A361959.
Cf. A361954, A361957 (not necessarily connected).

Programs

  • PARI
    \\ See PARI link in A361957 for program code.
{ my(A=A361958tabl(9)); for(i=1, #A, print(A[i, 1..i])) }

Formula

Column k is the inverse Euler transform of column k of A361957.

A361959 Number of connected unlabeled tiered posets with n elements.

Original entry on oeis.org

1, 1, 1, 3, 8, 25, 83, 330, 1538, 8834, 63723, 591313, 7180087, 115411088, 2472336977, 70840464484, 2720170935989, 140167035897433, 9702508891845883, 903305670556552694, 113233954374954246849, 19137449587197829494989, 4366006746295284220605007
Offset: 0

Views

Author

Andrew Howroyd, Apr 03 2023

Keywords

Comments

A tiered poset is a partially ordered set in which every maximal chain has the same length.

Links

Crossrefs

Row sums of A361958.
Cf. A361912 (not necessarily connected).

Programs

Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.