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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: [email protected]
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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

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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