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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.

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A050913 Pure 2-complexes on an infinite set of nodes with n multiple 2-simplexes. Also n-rowed binary matrices with all row sums 3, up to row and column permutation.

Original entry on oeis.org

1, 1, 4, 16, 93, 652, 6369, 79568, 1256425, 24058631, 543204998, 14138916124, 417362929209, 13798729189578, 505990335048034, 20415765544541866, 900364519682003919, 43155049922002494115, 2236988329443856718604, 124862936181977439454012, 7476052709321753156375756, 478506183522725779096476581, 32638841238874891261354722405, 2365895836144423508306322639848, 181785988254681334224483607437510, 14771116583797935886529061991645404, 1266545494725474774697216198539818982
Offset: 0

Views

Author

Vladeta Jovovic, Dec 29 1999

Keywords

Links

Crossrefs

Row n=3 of A331461.
Cf. A050911, A050912, A001400, A014395, A082789, A082790, A058790.

Extensions

More terms from T. Forbes (anthony.d.forbes(AT)googlemail.com), May 24 2003

A058790 Number of covers of an unlabeled n-set such that every point of the set is covered by exactly 3 subsets of the cover and that intersection of every 3 subsets of the cover contains at most one point.

Original entry on oeis.org

1, 3, 12, 66, 445, 4279, 53340, 846254, 16333946, 371976963, 9763321109, 290473143807, 9674133467729, 357177322891321, 14503958827502886, 643502334799711633, 31018731336031551119, 1616523352051185316626, 90689288905913623412837, 5456178840303106057314759, 350830170593891706361540379
Offset: 1

Views

Author

Vladeta Jovovic, Nov 30 2000

Keywords

Comments

Cover may include multiple occurrences of a subset. Also n-rowed binary matrices with distinct rows and all row sums 3.

References

  • For labeled case see Goulden I. P., Jackson D. M., Combinatorial Enumeration, John Wiley and Sons, New York, 1983.

Links

Crossrefs

Row n=3 of A331508.
Cf. A050535, A050913, A058783, A058784, A058785, A082789, A082790.

Extensions

More terms from T. Forbes (anthony.d.forbes(AT)googlemail.com), May 24 2003

A082789 Number of nonisomorphic configurations of n triples in Steiner triple systems.

Original entry on oeis.org

1, 2, 5, 16, 56, 282, 1865, 17100, 207697, 3180571
Offset: 1

Views

Author

T. Forbes (anthony.d.forbes(AT)googlemail.com), May 24 2003

Keywords

Comments

A configuration is a set of triples (of points) where every pair of points occurs in at most one triple. (A Steiner triple system is a set of triples where every pair occurs exactly once; thus configurations are often called partial Steiner triple systems.) The triples are also called blocks.
A 'generator' is 'a configuration where every point occurs in at least two blocks'. The term refers to the work of Horak, Phillips, Wallis & Yucas, who show that the number of occurrences of a configuration in a Steiner triple system is expressible as a linear form in the numbers of occurrences of the generators.
If we relax the restriction on the number of times a pair of points can occur in a configuration -- so that a configuration is just any multi-set of triples - then we get A050913.
If we allow a configuration to be any *set* of triples -- i.e., configurations with multiple occurrences of blocks are not allowed, but more than one pair is allowed -- then we get A058790.

Examples

			The five configurations of 3 triples are
.
     *---*---*       *---*---*
     *---*---*       *---*---*
     *---*---*        \
                       *
                        \
          *       *      *
         / \     /
        *   *   *                *
       /     \ /                /|
      *       *                * |
                              /  |
     *---*---*---*---*       *   *
              \               \  |
               *               * |
                \               \|
                 *               *

References

  • Mike Grannell and Terry Griggs, 'Configurations in Steiner triple systems', in Combinatorial Designs and their Applications, Chapman & Hall, CRC Research Notes in Math. 403 (1999), 103-126.
  • Horak, P., Phillips, N. K. C., Wallis, W. D. and Yucas, J. L., Counting frequencies of configurations in Steiner triple systems. Ars Combin. 46 (1997), 65-75.

Links

Crossrefs

Cf. A082790, A050913, A058790.
Showing 1-3 of 3 results.

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