Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 11
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Branden, Petter 2015. Handbook of Enumerative Combinatorics.

    Scott, Alexander D. and Sokal, Alan D. 2014. Complete monotonicity for inverse powers of some combinatorially defined polynomials. Acta Mathematica, Vol. 213, Issue. 2, p. 323.

    Kahn, J. and Neiman, M. 2012. Conditional negative association for competing urns. Random Structures & Algorithms, Vol. 41, Issue. 2, p. 262.

    Kahn, J. and Neiman, M. 2011. A strong log-concavity property for measures on Boolean algebras. Journal of Combinatorial Theory, Series A, Vol. 118, Issue. 6, p. 1749.

    Brändén, Petter and González D'León, Rafael S. 2010. On the half-plane property and the Tutte group of a matroid. Journal of Combinatorial Theory, Series B, Vol. 100, Issue. 5, p. 485.

    Kahn, J. and Neiman, M. 2010. Negative correlation and log-concavity. Random Structures & Algorithms, Vol. 37, Issue. 3, p. 367.

    Wagner, David G. and Wei, Yehua 2009. A criterion for the half-plane property. Discrete Mathematics, Vol. 309, Issue. 6, p. 1385.

    Choe, YoungBin 2008. A combinatorial proof of the Rayleigh formula for graphs. Discrete Mathematics, Vol. 308, Issue. 24, p. 5944.

    COCKS, CLIFFORD C. 2008. Correlated Matroids. Combinatorics, Probability and Computing, Vol. 17, Issue. 04,

    SEMPLE, CHARLES and WELSH, DOMINIC 2008. Negative Correlation in Graphs and Matroids. Combinatorics, Probability and Computing, Vol. 17, Issue. 03,

    Brändén, Petter 2007. Polynomials with the half-plane property and matroid theory. Advances in Mathematics, Vol. 216, Issue. 1, p. 302.

  • Combinatorics, Probability and Computing, Volume 15, Issue 5
  • September 2006, pp. 765-781

Rayleigh Matroids

  • DOI:
  • Published online: 31 July 2006

Motivated by a property of linear resistive electrical networks, we introduce the class of Rayleigh matroids. These form a subclass of the balanced matroids defined by Feder and Mihail [9] in 1992. We prove a variety of results relating Rayleigh matroids to other well-known classes – in particular, we show that a binary matroid is Rayleigh if and only if it does not contain $\mathcal{S}_{8}$ as a minor. This has the consequence that a binary matroid is balanced if and only if it is Rayleigh, and provides the first complete proof in print that $\mathcal{S}_{8}$ is the only minor-minimal binary non-balanced matroid, as claimed in [9]. We also give an example of a balanced matroid which is not Rayleigh.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
Please enter your name
Please enter a valid email address
Who would you like to send this to? *