Rayleigh matroids

Combinatorics Probability and Computing

Volumn 15, Issue 5, 2006, Pages 765-781

  Choe, Youngbin ^a   Wagner, David G ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC RESISTANCE; MATHEMATICAL MODELS; MATRIX ALGEBRA;

BALANCED MATROIDS; LINEAR RESISTIVE ELECTRICAL NETWORKS; RAYLEIGH MATROIDS;

ELECTRIC NETWORK ANALYSIS;

EID: 33746661189     PISSN: 09635483     EISSN: 14692163     Source Type: Journal    
DOI: 10.1017/S0963548306007541     Document Type: Article

References (25)

1. Balabanian, N. and Bickart, T. A. (1969) Electrical Network Theory, Wiley, New York.
2. Brooks, R. L., Smith, C. A. B., Stone, A. H. and Tutte, W. T. (1940) The dissection of rectangles into squares. Duke Math. J. 7 312-340.
3. Bruter, C. P. (1971) Déformations des matroïdes. CR Acad. Sci. Paris Sér. A-B 273 A9-A10.
4. Chavez Lomelí, L. E. (1994) The basis problem for matroids. MSc thesis, University of Oxford.
5. Choe, Y.-B. (2003) Polynomials with the half-plane property and Rayleigh monotonicity. PhD thesis, University of Waterloo.
6. Choe, Y.-B. Rayleigh monotonicity of sixth-root of unity matroids. In preparation.
7. Choe, Y.-B., Oxley, J. G., Sokal, A. D. and Wagner, D. G. (2004) Homogeneous polynomials with the half-plane property. Adv. Appl. Math. 32 88-187.
8. Corp, J. and McNulty, J. (2001) On a characterization of balanced matroids. Ars Combin. 58 111-112.
9. Feder, T. and Mihail, M. (1992) Balanced matroids. In Proc. 24th Annual ACM (STOC), Victoria BC, ACM Press, New York.
10. Fettweis, A. and Basu, S. (1987) New results on stable multidimensional polynomials, Part I: Continuous case. IEEE Trans. Circuits Systems 34 1221-1232.
11. Godsil, C. D. (1984) Real graph polynomials. In Progress in Graph Theory (Waterloo, Ont., 1982), Academic Press, Toronto, pp. 281-293.
12. Harary, F. and Lindström, B. (1981) On balance in signed matroids. J. Combin. Inform. System Sci. 6 123-128.
13. Hardy, G. H., Littlewood, J. E. and Pólya, G. (1988) Inequalities, reprint of the 1952 edition, Cambridge University Press, Cambridge.
14. Kirchhoff, G. (1847) Über die Auflösung der Gleichungen, auf welche man bei der Untersuchungen der linearen Vertheilung galvanischer Ströme geführt wird. Ann. Phys. Chem. 72 497-508.
15. Lyons, R. D. (2003) Determinantal probability measures. Publ. Math. Inst. Hautes Études Sci. 98 167-212.
16. Merino, C. (1999) Matroids, the Tutte polynomial and the chip firing game. PhD thesis, Somerville College, University of Oxford.
17. Mihail, M. and Vazirani, U. (1989) On the expansion of 0-1 polytopes. Technical Report 05-89, Harvard University.
18. Oxley, J. G. (1992) Matroid Theory, Oxford University Press, New York.
19. Pemantle, R. (2000) Toward a theory of negative dependence. J. Math. Phys. 41 1371-1390.
20. Seymour, P. D. (1980) Matroids and multicommodity flows. Europ. J. Combin. 1 257-290.
21. Seymour, P. D. and Welsh, D. J. A. (1975) Combinatorial applications of an inequality from statistical mechanics. Math. Proc. Camb. Phil. Soc. 75 495-495.
22. Stanley, R. P. (1981) Two combinatorial applications of the Aleksandrov-Fenchel inequalities. J. Combin. Theory Ser. A 31 56-65.
23. Wagner, D. G. (2005) Rank three matroids are Rayleigh. Electronic J. Combin. 12 N8 1-11.
24. Wagner, D. G. (2005) Matroid inequalities from electrical network theory. Electronic J. Combin. 11 Al 1-17.
25. Whittle, G. (1997) On matroids representable over GF(3) and other fields. Trans. Amer. Math. Soc. 349 579-603.