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All unconstrained information inequalities in three or fewer random variables are known to be "Shannon-type", in that they are nonnegative linear combinations of instances of the inequality I(A;B|C) ges 0. In 1998, Zhang and Yeung gave the first example of an information inequality in four variables that is not "Shannon-type". Here we give six new… (More)

- R Dougherty, C Freiling, K Zeger
- 2008

The following typographical errors appeared in this publication: • On page 1959, column 2, in the 2nd line of Step 3, the equality g(x) = n 1 should be g(ˆ x) = n 1. • On page 1962, column 1, in the 6th line after Table IV, the period after " Finally " should be a comma. • On page 1965, column 2, in the 1st line before Section VII, the text " that " should… (More)

— The well-studied Vámos matroid has provided a wealth of interesting theoretical results in matroid theory. We use the Vámos matroid to construct a new network, which we call the Vámos network. We then exploit the Vámos network to answer in the negative the open question as to whether Shannon-type information inequalities are in general sufficient for… (More)

— We define a class of networks, called matroidal networks, which includes as special cases all scalar-linearly solv-able networks, and in particular solvable multicast networks. We then present a method for constructing matroidal networks from known matroids. We specifically construct networks that play an important role in proving results in the… (More)

- I N V I T E D P A P, Randall Dougherty, Chris Freiling, Kenneth Zeger
- 2011

2 Matroid Theory 3 This paper explores the connection between network coding and matroid theory, 4 a branch of mathematics that generalizes linear algebra and graph theory. ABSTRACT | Networks derived from matroids have played a 7 fundamental role in proving theoretical results about the limits 8 of network coding. In this tutorial paper, we review many… (More)

The well-studied Vámos matroid has provided a wealth of interesting theoretical results in matroid theory. We use the Vámos matroid to construct a new network, which we call the Vámos network. We then exploit the Vámos network to answer in the negative the open question as to whether Shannon-type information inequalities are in general… (More)