|
%I #70 Sep 13 2023 23:18:18
%S 1,2,4,8,17,38,98,306,1724,383172
%N Number of unlabeled matroids on n points.
%C This is the total number of pairwise non-isomorphic (i.e., "unlabeled") matroids on n points, with no restrictions on loops, parallel elements etc.
%C Partial sums of A058718. - _Jonathan Vos Post_, Apr 25 2010
%D J. G. Oxley, Matroid Theory. Oxford, England: Oxford University Press, 1993. See p. 473.
%H Dragan M. Acketa, <a href="https://sites.dmi.uns.ac.rs/nsjom/Papers/08/NSJOM_08_083_090.pdf">On the enumeration of matroids of rank-2</a>, Zbornik radova Prirodnomatematickog fakulteta-Univerzitet u Novom Sadu 8 (1978): 83-90. - _N. J. A. Sloane_, Dec 04 2022
%H Jayant Apte and J. M. Walsh, <a href="http://arxiv.org/abs/1605.04598">Constrained Linear Representability of Polymatroids and Algorithms for Computing Achievability Proofs in Network Coding</a>, arXiv preprint arXiv:1605.04598 [cs.IT], 2016-2017.
%H Jesus DeLoera, Yvonne Kemper, and Steven Klee, <a href="http://arxiv.org/abs/1106.2576">h-vectors of small matroid complexes</a>, arXiv:1106.2576 [math.CO], 2011.
%H W. M. B. Dukes, <a href="https://arxiv.org/abs/math/0411557">The number of matroids on a finite set</a>, arXiv:math/0411557 [math.CO], 2004.
%H W. M. B. Dukes, <a href="http://emis.impa.br/EMIS/journals/SLC/wpapers/s51dukes.html">On the number of matroids on a finite set</a>, Séminaire Lotharingien de Combinatoire 51 (2004), Article B51g.
%H S. C. Locke, <a href="http://euler.math.fau.edu/locke/SmallMatroids.htm">Matroids</a>
%H Dillon Mayhew and Gordon F. Royle, <a href="https://arxiv.org/abs/math/0702316">Matroids with nine elements</a>, arXiv:math/0702316 [math.CO], 2007.
%H Dillon Mayhew and Gordon F. Royle, <a href="https://doi.org/10.1016/j.jctb.2007.07.005">Matroids with nine elements</a>, J. Combin. Theory Ser. B 98(2) (2008), 415-431.
%H Gordon Royle and Dillon Mayhew, <a href="https://web.archive.org/web/20080828102733/http://people.csse.uwa.edu.au/gordon/matroid-integer-sequences.html">9-element matroids</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Matroid.html">Matroid</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphVertex.html">Graph Vertex</a>.
%H D. J. A. Welsh, <a href="http://dx.doi.org/10.1016/S0021-9800(69)80094-3">A bound for the number of matroids</a>, J. Combinat. Theory, Ser. A, 6 (1969), 313-316. - From _N. J. A. Sloane_, May 06 2012
%H <a href="/index/Mat#matroid">Index entries for sequences related to matroids</a>
%Y Cf. A002773, A058673 (labeled matroids), A058718.
%Y Row sums of A053534.
%K nonn,nice,more
%O 0,2
%A _Eric W. Weisstein_
%E a(9) from _Gordon Royle_, Dec 23 2006
%E Name clarified by _Lorenzo Sauras Altuzarra_, Aug 10 2023
| 