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Any unconstrained information inequality in three or fewer random variables can be written as a linear combination of instances of Shannon's inequality I(A;B|C) >= 0 .
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Z. Zhang and R. W. Yeung, “A non-Shannon-type conditional inequality of information quantities”, Proc. IEEE Transactions on Information Theory
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Z. Zhang and R. W. Yeung, “On characterization of entropy function via information inequalities”, Proc. IEEE Transactions on Information Theory
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K. Makarychev, Y. Makarychev, A. Romashchenko, and N. Vereshchagin, “A new class of non-Shannon-type inequalities for entropies”, Communications in Information and Systems
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Z. Zhang, “On a new non-Shannon type information inequality”, Communications in Information and Systems
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R. Dougherty, C. Freiling, and K. Zeger, “Six new non-Shannon information inequalities”, Proc. IEEE International Symposium on Information Theory, (ISIT), 2006,
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MATLAB, commercially available software package by The Math Works, website: http://www.mathworks.com/
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R. W. Yeung and Y. O. Yan, Information Theory Inequality Prover (ITIP), software, website: http://user-www.ie.cuhk.edu.hk/ ITIP/
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T. Chan and A. Grant, Entropy vectors and network codes, Proc. IEEE International Symposium on Information Theory, (ISIT), 2007,
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R. Dougherty, C. Freiling, and K. Zeger, “Matroids, networks, and non-Shannon information inequalities”, Proc. IEEE Transactions on Information Theory
2007
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F. Matus, “Infinitely many information inequalities”, Proc. IEEE International Symposium on Information Theory, (ISIT), 2007,
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W. Xu, J. Wang, and J. Sun, “A projection method for derivation of non-Shannon-type information inequalities”, Proc. IEEE International Symposium on Information Theory, (ISIT), 2008,
2008
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