We show that the space of all binary Huffman codes for a finite alphabet defines a lattice, ordered by the imbalance of the code trees. Representing code trees as path-length sequences, we show that the imbalance ordering is closely related to a majorization ordering on real-valued sequences that correspond to discrete probability density functions. Furthermore, this tree imbalance is a partial...

In this paper we study the departure processes of two rate-control throttles: the token bank and the leaky bucket. Using sample path methods and the notion of majorization, we analyze the eeect that parameters such as the token buuer capacity and token generation period have on the vector of interdeparture times. In the transient case, we establish the monotonicity of the burst reduction in the...

We consider the properties of the Shannon entropy for two probability distributions which stand in the relationship of majorization. Then we give a generalization of a theorem due to Uhlmann, extending it to infinite dimensional Hilbert spaces. Finally we show that for any quantum channel Φ, one has S(Φ(ρ)) = S(ρ) for all quantum states ρ if and only if there exists an isometric operator V such...