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Rayleigh matroids
 COMBIN. PROB. COMPUT
, 2003
"... 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 [10] in 1992. We prove a variety of results relating Rayleigh matroids to other well–known classes – in particular ..."
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Cited by 8 (1 self)
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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 [10] in 1992. We prove a variety of results relating Rayleigh matroids to other well–known classes
Rank–three matroids are Rayleigh
, 2005
"... A Rayleigh matroid is one which satisfies a set of inequalities analogous to the Rayleigh monotonicity property of linear resistive electrical networks. We show that every matroid of rank three satisfies these inequalities. ..."
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A Rayleigh matroid is one which satisfies a set of inequalities analogous to the Rayleigh monotonicity property of linear resistive electrical networks. We show that every matroid of rank three satisfies these inequalities.
Rank three matroids are Rayleigh
"... Abstract. A Rayleigh matroid is one which satisfies a set of inequalities analogous to the Rayleigh monotonicity property of linear resistive electrical networks. We show that every matroid of rank three satisfies these inequalities. 1. Introduction. (For the basic concepts of matroid theory we refe ..."
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Cited by 2 (0 self)
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Abstract. A Rayleigh matroid is one which satisfies a set of inequalities analogous to the Rayleigh monotonicity property of linear resistive electrical networks. We show that every matroid of rank three satisfies these inequalities. 1. Introduction. (For the basic concepts of matroid theory we
An extension of matroid rank submodularity and the ZRayleigh property
, 2011
"... We define an extension of matroid rank submodularity called Rsubmodularity, and introduce a minorclosed class of matroids called extended submodular matroids that are wellbehaved with respect to Rsubmodularity. We apply Rsubmodularity to study a class of matroids with negatively correlated mult ..."
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multivariate Tutte polynomials called the ZRayleigh matroids. First, we show that the class of extended submodular matroids are ZRayleigh. Second, we characterize a minorminimal nonZRayleigh matroid using its Rsubmodular properties. Lastly, we use Rsubmodularity to show that the Fano and non
Capacity of Fading Channels with Channel Side Information
, 1997
"... We obtain the Shannon capacity of a fading channel with channel side information at the transmitter and receiver, and at the receiver alone. The optimal power adaptation in the former case is "waterpouring" in time, analogous to waterpouring in frequency for timeinvariant frequencysele ..."
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Cited by 579 (23 self)
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We obtain the Shannon capacity of a fading channel with channel side information at the transmitter and receiver, and at the receiver alone. The optimal power adaptation in the former case is "waterpouring" in time, analogous to waterpouring in frequency for timeinvariant frequencyselective fading channels. Inverting the channel results in a large capacity penalty in severe fading.
NEGATIVE CORRELATION IN GRAPHS AND MATROIDS
, 2005
"... The following two conjectures arose in the work of Grimmett and Winkler, and Pemantle: the uniformly random forest F and the uniformly random connected subgraph C of a finite graph G have the edgenegativeassociation property. In other words, for all distinct edges e and f of G, the probability tha ..."
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Cited by 5 (0 self)
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, we describe an infinite, nontrivial class of graphs and matroids for which a generalized version of both conjectures holds.
A Combinatorial proof of Rayleigh formula for graphs
"... Rayleigh monotonicity in Physics has a combinatorial interpretation. In this paper we give a combinatorial proof of the Rayleigh formula using Jacobi Identity and All Minors MatrixTree Theorem. Motivated by the fact that the edge set of each spanning tree of G is a basis of the graphic matroid indu ..."
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Cited by 3 (0 self)
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Rayleigh monotonicity in Physics has a combinatorial interpretation. In this paper we give a combinatorial proof of the Rayleigh formula using Jacobi Identity and All Minors MatrixTree Theorem. Motivated by the fact that the edge set of each spanning tree of G is a basis of the graphic matroid
Matroid inequalities from electrical network theory
 ELECTRON. J. COMBIN
, 2005
"... In 1981, Stanley applied the Aleksandrov–Fenchel Inequalities to prove a logarithmic concavity theorem for regular matroids. Using ideas from electrical network theory we prove a generalization of this for the wider class of matroids with the “half–plane property”. Then we explore a nest of inequali ..."
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Cited by 12 (4 self)
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In 1981, Stanley applied the Aleksandrov–Fenchel Inequalities to prove a logarithmic concavity theorem for regular matroids. Using ideas from electrical network theory we prove a generalization of this for the wider class of matroids with the “half–plane property”. Then we explore a nest
ON THE HALFPLANE PROPERTY AND THE TUTTE GROUP OF A MATROID
, 2010
"... A multivariate polynomial is stable if it is nonvanishing whenever all variables have positive imaginary parts. A matroid has the weak halfplane property (WHPP) if there exists a stable polynomial with support equal to the set of bases of the matroid. If the polynomial can be chosen with all of i ..."
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Cited by 5 (2 self)
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A multivariate polynomial is stable if it is nonvanishing whenever all variables have positive imaginary parts. A matroid has the weak halfplane property (WHPP) if there exists a stable polynomial with support equal to the set of bases of the matroid. If the polynomial can be chosen with all
Results 1  10
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161