Collection Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme
Organisateur(s)
Date(s)
19/05/2024
Partition-Symmetrical Entropy Functions
De Qi Chen
Let N={1,…,n}. Let p={N1,…,Nt} be a t-partition of N. An entropy function h is called p-symmetrical if for all A, B⊂N, h(A)=h(B) whenever |A∩Ni|=|B∩Ni|, i=1,…,t. We prove that the closure of the set of p-symmetrical entropy functions is completely characterized by Shannon-type information inequalities if and only if p is the 1-partition or a 2-partition with one of its blocks being a singleton. The characterization of the partition-symmetrical entropy functions can be useful for solving some information theory and related problems where symmetry exists in the structure of the problems.
