Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-26T07:50:56.080Z Has data issue: false hasContentIssue false
  • English
  • Français

Small Submatroids in Random Matroids

Published online by Cambridge University Press:  12 September 2008

Wojciech Kordecki
Wojciech Kordecki
Affiliation:
Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50–370 Wrocław, Poland Email: kordecki@graf.im.pwr.wroc.pl
Get access Rights & Permissions [Opens in a new window]

Abstract

Let M be a matroid and let Xr count copies of M in a random matroid of rank r. The Poisson and normal convergence of Xr are investigated under some restriction.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 3 , September 1996 , pp. 257 - 266
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Ruciński, A. (1988) When are small subgraphs of a random graph normally distributed? Prob. Theory Rel. Fields 78CrossRefGoogle Scholar
[2]Ruciński, A. (1990) Small subgraphs of random graphs – a survey. Random Graphs'87 (Proceedings, Poznań, 1987). Wiley, pp. 283–303.Google Scholar
[3]Welsh, D. J. A. (1976) Matroid Theory. London Math. Soc. Monographs No.8. Academic Press.Google Scholar
[4]Voigt, B. (1986) On the evolution of finite affine and projective spaces. Math. Oper. Res. 49 313–327.Google Scholar
[5]Kelly, D. G. and Oxley, J. G. (1982) Asymptotic properties of random subsets of projective spaces. Math. Proc. Cambridge Phil. Soc. 91 119–130.CrossRefGoogle Scholar
[6]Narayanan, H. and Vartak, N. (1981) On molecular and atomic matroids. In: Combinatorics and Graph Theory (ed. Rao, S. B.). Lecture Notes in Math. 885, Springer-Verlag, pp. 358–364.CrossRefGoogle Scholar
[7]Cunnigham, W. H. (1985) Optimal attack and reinforcement of a network. J. Assoc. Comp. Math. 32 549–561.CrossRefGoogle Scholar
[8]Catlin, P. A., Grossman, J. W., Hobbs, A. M. and Hong-Jian, Lai (1989) Fractional arboricity, strength, principal partitions in graphs and matroids. Combinatorics & Optimization. Res. Report CORR 89–13, Combinatorics & Optimization.Google Scholar
[9]Bollobás, B. (1981) Threshold functions for small subgraphs. Math. Proc. Cambridge Phil. Soc. 90 197–206.CrossRefGoogle Scholar
[10]Oxley, J. G. (1984) Threshold distribution function for some random representable matroids. Math. Proc. Cambridge Phil. Soc. 95 335–346.CrossRefGoogle Scholar
[11]Janson, S., Łuczak, T. and Ruciński, A. (1990) An exponential bound for the probability of nonexistence of a specified subgraphs in a random graph. Random Graphs'87 (Proceedings, Poznań, 1987) (Proceedings, Poznań, 1987), Wiley, 73–87.Google Scholar
[12]Janson, S. (1990) Poisson approximation for large deviation. Random Struc. Alg. 1 221–229.CrossRefGoogle Scholar
[13]Barbour, A. D., Hoist, L. and Janson, S. (1992) Poisson Approximation. Oxford Science Publication, Clarendon. Press.CrossRefGoogle Scholar
[14]Kordecki, W. (1988) Strictly balanced submatroids in random subsets of projective geometries. Coll. Math. LV 371–375.CrossRefGoogle Scholar
[15]Janson, S. (1988) Normal convergence by higher semi-invariants with applications to sums of dependent random variables and random graphs. Ann. Probab. 16 305–312.CrossRefGoogle Scholar
[16]Mikhailov, V. G. (1991) On a Janson's theorem. Teor. Verojatn. i ee Prim. 36 168–170 (in Russian).Google Scholar
[17]Ruciński, A. (1992) Proving normality in combinatorics. Random Graphs'89 (Proceedings, Poznań, 1989). Wiley, 215–231.Google Scholar