Adhesivity of polymatroids

Discrete Mathematics

Volumn 307, Issue 21, 2007, Pages 2464-2477

  Matúš, František ^a  

^a INSTITUTE OF INFORMATION THEORY AND AUTOMATION   (Czech Republic)

Author keywords

Entropy function; Gluing; Ingleton inequality; Matroid; Modular pair; Non Shannon information theoretical inequality; Pasting; Polymatroid; Proper amalgam; Zhang Yeung inequality

Indexed keywords

CONES; FINITE DIFFERENCE METHOD; NUMERICAL METHODS; SET THEORY;

NON-SHANNON INFORMATION THEORETICAL INEQUALITY; POLYMATROIDS; RANK FUNCTIONS; ZHANG-YEUNG INEQUALITIES;

MATRIX ALGEBRA;

EID: 34648831455     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disc.2006.11.013     Document Type: Article

References (21)

1. Dougherty R., Freiling C., and Zeger K. Six new non-Shannon information inequalities. IEEE International Symposium on Information Theory. Seattle, Washington (2006) 233-236
2. Fujishige S. Polymatroidal dependence structure of a set of random variables. Inform. and Control 39 (1978) 55-72
3. Fujishige S. Submodular Functions and Optimization (1991), North-Holland, Amsterdam
4. A.W. Ingleton, Conditions for representability and transversality of matroids, Proc. Fr. Br. Conf. 1970, Springer Lecture Notes, vol. 211, 1971, pp. 62-67.
5. Ingleton A.W. Representation of matroids. In: Welsh D.J.A. (Ed). Combinatorial Mathematics and its Applications (1971), Academic Press, London, New York 149-169
6. Lovász L. Submodular functions and convexity. In: Bachem A., Grötchel M., and Korte B. (Eds). Mathematical Programming-The State of the Art (1982), Springer, Berlin, Heidelberg, New York, Tokyo 234-257
7. Makarychev K., Makarychev Yu., Romashchenko A., and Vereshchagin N. A new class of non-Shannon-type inequalities for entropies. Commun. Inform. Systems 2 (2002) 147-166
8. Matúš F. Extreme convex set functions with many nonnegative differences. Discrete Math. 135 (1994) 177-191
9. Matúš F. Inequalities for Shannon entropies and adhesivity of polymatroids. Proceedings of the Ninth Canadian Workshop on Information Theory. McGill University, Montréal, Canada (2005) 28-31
10. F. Matúš, Two constructions on limits of entropy functions, IEEE Trans. Inform. Theory, 53 (2007) 320-330.
11. Matúš F., and Studený M. Conditional independences among four random variables I. Combin. Probab. Comput. 4 (1995) 269-278
12. Narayan H. Submodular Functions and Electrical Networks (1997), Elsevier, Amsterdam
13. Nguyen H.Q. Semimodular functions. In: White N. (Ed). Theory of Matroids (1986), Cambridge University Press, Cambridge, London 272-297
14. Oxley J.G. Matroid Theory (1992), Oxford University Press, Oxford, New York, Tokyo
15. Rockafellar R.T. Convex Analysis (1970), Princeton University Press, Princeton
16. Welsh D.J.A. Matroid Theory (1976), Academic Press, London
17. Yeung R.W. A First Course in Information Theory (2002), Kluwer Academic/Plenum Publishers, New York
18. Yeung R.W., and Zhang Z. A class of non-Shannon-type information inequalities and their applications. Commun. Inform. Systems 1 (2001) 87-100
19. Zhang Z. On a new non-Shannon-type information inequality. Commun. Inform. Systems 3 (2003) 47-60
20. Zhang Z., and Yeung R.W. On characterization of entropy function via information inequalities. IEEE Trans. Inform. Theory 44 (1998) 1440-1452
21. Ziegler G.M. Lectures on Polytopes, Graduate Texts in Mathematics vol. 152 (1998), Springer, New York, Berlin, Heidelberg