A058718 -id:A058718 - cp's OEIS frontend

A055545 Number of unlabeled matroids on n points.

1, 2, 4, 8, 17, 38, 98, 306, 1724, 383172

Offset: 0

This is the total number of pairwise non-isomorphic (i.e., "unlabeled") matroids on n points, with no restrictions on loops, parallel elements etc.

Partial sums of A058718. - Jonathan Vos Post, Apr 25 2010

J. G. Oxley, Matroid Theory. Oxford, England: Oxford University Press, 1993. See p. 473.

Dragan M. Acketa, On the enumeration of matroids of rank-2, Zbornik radova Prirodnomatematickog fakulteta-Univerzitet u Novom Sadu 8 (1978): 83-90. - _N. J. A. Sloane_, Dec 04 2022
Jayant Apte and J. M. Walsh, Constrained Linear Representability of Polymatroids and Algorithms for Computing Achievability Proofs in Network Coding, arXiv preprint arXiv:1605.04598 [cs.IT], 2016-2017.
Jesus DeLoera, Yvonne Kemper, and Steven Klee, h-vectors of small matroid complexes, arXiv:1106.2576 [math.CO], 2011.
W. M. B. Dukes, The number of matroids on a finite set, arXiv:math/0411557 [math.CO], 2004.
W. M. B. Dukes, On the number of matroids on a finite set, Séminaire Lotharingien de Combinatoire 51 (2004), Article B51g.
S. C. Locke, Matroids
Dillon Mayhew and Gordon F. Royle, Matroids with nine elements, arXiv:math/0702316 [math.CO], 2007.
Dillon Mayhew and Gordon F. Royle, Matroids with nine elements, J. Combin. Theory Ser. B 98(2) (2008), 415-431.
Gordon Royle and Dillon Mayhew, 9-element matroids.
Eric Weisstein's World of Mathematics, Matroid.
Eric Weisstein's World of Mathematics, Graph Vertex.
D. J. A. Welsh, A bound for the number of matroids, J. Combinat. Theory, Ser. A, 6 (1969), 313-316. - From _N. J. A. Sloane_, May 06 2012
Index entries for sequences related to matroids

Cf. A002773, A058673 (labeled matroids), A058718.

Row sums of A053534.

a(9) from Gordon Royle, Dec 23 2006

Name clarified by Lorenzo Sauras Altuzarra, Aug 10 2023

A058716 Triangle T(n,k) giving number of nonisomorphic loopless matroids of rank k on n labeled points (n >= 0, 0 <= k <= n).

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 4, 3, 1, 0, 1, 6, 9, 4, 1, 0, 1, 10, 25, 18, 5, 1, 0, 1, 14, 70, 85, 31, 6, 1, 0, 1, 21, 217, 832, 288, 51, 7, 1

Offset: 0

N. J. A. Sloane, Dec 31 2000

			Triangle T(n,k) (with rows n >= 0 and columns k >= 0) begins as follows:
  1;
  0, 1;
  0, 1,  1;
  0, 1,  2,   1;
  0, 1,  4,   3,   1;
  0, 1,  6,   9,   4,   1;
  0, 1, 10,  25,  18,   5,  1;
  0, 1, 14,  70,  85,  31,  6, 1;
  0, 1, 21, 217, 832, 288, 51, 7, 1;
  ...

W. M. B. Dukes, Tables of matroids.
W. M. B. Dukes, Counting and Probability in Matroid Theory, Ph.D. Thesis, Trinity College, Dublin, 2000.
W. M. B. Dukes, The number of matroids on a finite set, arXiv:math/0411557 [math.CO], 2004.
W. M. B. Dukes, On the number of matroids on a finite set, Séminaire Lotharingien de Combinatoire 51 (2004), Article B51g.
Index entries for sequences related to matroids

Cf. A058717 (same except for border), A058710, A058711. Row sums give A058718. Diagonals give A000065, A058719.

Corrected and extended by Jean-François Alcover, Oct 21 2013

Reverted to original data by Sean A. Irvine, Aug 16 2022

A058717 Triangle T(n,k) giving number of nonisomorphic loopless matroids of rank k on n labeled points (n >= 1, 1<=k<=n).

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 6, 9, 4, 1, 1, 10, 25, 18, 5, 1, 1, 14, 70, 85, 31, 6, 1, 1, 21, 217, 832, 288, 51, 7, 1

Offset: 1

N. J. A. Sloane, Dec 31 2000

			1;
1,  1;
1,  2,   1;
1,  4,   3,   1;
1,  6,   9,   4,   1;
1, 10,  25,  18,   5,  1;
1, 14,  70,  85,  31,  6, 1;
1, 21, 217, 832, 288, 51, 7, 1;
...

W. M. B. Dukes, Tables of matroids
W. M. B. Dukes, Counting and Probability in Matroid Theory, Ph.D. Thesis, Trinity College, Dublin, 2000.
Index entries for sequences related to matroids
W. M. B. Dukes, On the number of matroids on a finite set

Cf. A058716 (same except for border), A058710, A058711.

Row sums give A058718. Diagonals give A000065, A058719.

Corrected and extended by Jean-François Alcover, Oct 21 2013

Reverted to original data by Jean-François Alcover, Aug 17 2022

cp's OEIS Frontend

A055545 Number of unlabeled matroids on n points.

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A058716 Triangle T(n,k) giving number of nonisomorphic loopless matroids of rank k on n labeled points (n >= 0, 0 <= k <= n).

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A058717 Triangle T(n,k) giving number of nonisomorphic loopless matroids of rank k on n labeled points (n >= 1, 1<=k<=n).

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Author

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Examples

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Extensions