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On group violations of inequalities in five subgroups
1. | Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore |
References:
[1] |
T. H. Chan and R. W. Yeung, On a relation between information inequalities and group theory, IEEE Trans. Inform. Theory, 48 (2002), 1992-1995.
doi: 10.1109/TIT.2002.1013138. |
[2] |
R. Dougherty, C. Freiling and K. Zeger, Linear rank inequalities on five or more variables, preprint, arXiv:0910.0284 |
[3] |
D. S. Dummit and R. M. Foote, Abstract Algebra, Hoboken, Wiley, 2004. |
[4] |
C. F. Gardiner, A First Course in Group Theory, Springer, 2013. |
[5] |
D. Hammer, A. Romashchenko, A. Shen and N. Vereshchagin, Inequalities for Shannon entropy and Kolmogorov complexity, in Proc. 12th Ann. IEEE Conf. Comp. Compl., IEEE, 1997, 13-23.
doi: 10.1109/CCC.1997.612296. |
[6] |
B. Hassibi and S. Shadbakht, Normalized entropy vectors, network information theory and convex optimization, in 2007 Inform. Theory Workshop (ITW 2007), 2007. |
[7] |
A. Ingleton, Representation of matroids, Combin. Math. Appl., (1971), 23. |
[8] |
H. Mann, Additive group theory - a progress report, Bull. Amer. Math. Soc., 79 (1973), 1069-1075. |
[9] |
W. Mao and B. Hassibi, Violating the Ingleton inequality with finite groups, in 47th Ann. Allerton Conf. Commun. Contr. Comp., IEEE, 2009, 1053-1060. |
[10] |
N. Markin, E. Thomas and F. Oggier, Groups and information inequalities in 5 variables, in Allerton'14 Proc. 52nd Ann. Allerton Conf. Commun. Control Comp., IEEE, 2013, 804-809. |
[11] |
F. Matús, Conditional independences among four random variables I, Combin. Prob. Comp., 4 (1995), 269-278.
doi: 10.1017/S0963548300001644. |
[12] |
J. J. Rotman, An Introduction to the Theory of Groups, Springer, 1999.
doi: 10.1007/978-1-4612-4176-8. |
[13] |
J.-P. Serre, Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math., 15 (1971), 259-331. |
[14] |
E. K. Thomas, N. Markin and F. Oggier, On Abelian Group Representability of Finite Groups, Adv. Math. Commun., 8 (2014), 139-152.
doi: 10.3934/amc.2014.8.139. |
[15] |
X. Yan, R. Yeung and Z. Zhang, The capacity for multi-source multi-sink network coding, in 2007 Int. Symp. Inform. Theory (ISIT 2007), Nice, 2007. |
show all references
References:
[1] |
T. H. Chan and R. W. Yeung, On a relation between information inequalities and group theory, IEEE Trans. Inform. Theory, 48 (2002), 1992-1995.
doi: 10.1109/TIT.2002.1013138. |
[2] |
R. Dougherty, C. Freiling and K. Zeger, Linear rank inequalities on five or more variables, preprint, arXiv:0910.0284 |
[3] |
D. S. Dummit and R. M. Foote, Abstract Algebra, Hoboken, Wiley, 2004. |
[4] |
C. F. Gardiner, A First Course in Group Theory, Springer, 2013. |
[5] |
D. Hammer, A. Romashchenko, A. Shen and N. Vereshchagin, Inequalities for Shannon entropy and Kolmogorov complexity, in Proc. 12th Ann. IEEE Conf. Comp. Compl., IEEE, 1997, 13-23.
doi: 10.1109/CCC.1997.612296. |
[6] |
B. Hassibi and S. Shadbakht, Normalized entropy vectors, network information theory and convex optimization, in 2007 Inform. Theory Workshop (ITW 2007), 2007. |
[7] |
A. Ingleton, Representation of matroids, Combin. Math. Appl., (1971), 23. |
[8] |
H. Mann, Additive group theory - a progress report, Bull. Amer. Math. Soc., 79 (1973), 1069-1075. |
[9] |
W. Mao and B. Hassibi, Violating the Ingleton inequality with finite groups, in 47th Ann. Allerton Conf. Commun. Contr. Comp., IEEE, 2009, 1053-1060. |
[10] |
N. Markin, E. Thomas and F. Oggier, Groups and information inequalities in 5 variables, in Allerton'14 Proc. 52nd Ann. Allerton Conf. Commun. Control Comp., IEEE, 2013, 804-809. |
[11] |
F. Matús, Conditional independences among four random variables I, Combin. Prob. Comp., 4 (1995), 269-278.
doi: 10.1017/S0963548300001644. |
[12] |
J. J. Rotman, An Introduction to the Theory of Groups, Springer, 1999.
doi: 10.1007/978-1-4612-4176-8. |
[13] |
J.-P. Serre, Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math., 15 (1971), 259-331. |
[14] |
E. K. Thomas, N. Markin and F. Oggier, On Abelian Group Representability of Finite Groups, Adv. Math. Commun., 8 (2014), 139-152.
doi: 10.3934/amc.2014.8.139. |
[15] |
X. Yan, R. Yeung and Z. Zhang, The capacity for multi-source multi-sink network coding, in 2007 Int. Symp. Inform. Theory (ISIT 2007), Nice, 2007. |
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