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- Chris Freiling
- J. Symb. Log.
- 1986

- Ray C . Dougherty, Chris Freiling, Kenneth Zeger
- 2006 IEEE International Symposium on Information…
- 2006

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)

- Hajrudin Fejzic, Chris Freiling, Dan Rinne
- The American Mathematical Monthly
- 2009

For any C ⊆ R there is a subset A ⊆ C such that A + A has inner measure zero and outer measure the same as C + C. Also, there is a subset A of the Cantor middle third set such that A+A is Bernstein in [0, 2]. On the other hand there is a perfect set C such that C + C is an interval I and there is no subset A ⊆ C with A + A Bernstein in I.

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)

- Chris Freiling, Miklós Laczkovich, Dan Rinne
- Discrete & Computational Geometry
- 1997

- Chris Freiling, Robert Hunter, Cynthia Turner, Russell Wheeler
- The American Mathematical Monthly
- 2000

We define a class of networks, called matroidal networks, which includes as special cases all scalar-linearly solvable 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 literature,… (More)

- Ray C . Dougherty, Chris Freiling, Kenneth Zeger
- 2006 4th International Symposium on Modeling and…
- 2006

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)

- Chris Freiling
- Bulletin of Symbolic Logic
- 1995

The roots of this problem go back to the beginnings of calculus and it is even sometimes called “Newton’s problem”. Historically, it has played a major role in the development of the theory of the integral. For example, it was Lebesgue’s primary motivation behind his theory of measure and integration. Indeed, the Lebesgue integral solves the primitive… (More)