Speaker: Chen Qi

Title: Partition-Symmetrical Entropy Functions

Abstract: Let $N=\{1, \cdots, n\}$. Let $p=\{N_1, \cdots, N_t\}$ be a $t$-partition of $N$. An entropy function $h$ is called $p$-symmetrical if for all $A, B\subset N$, $h(A)=h(B)$ whenever $|A\cap N_i|=|B\cap N_i|$, $i=1,\cdots,t$. 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.