Extrema in majorization order with applications to entropic continuity bounds

An essay submitted in the competition for a Smith-Knight or Rayleigh-Knight prize. This essay combines my work on uniform continuity bounds (arXiv:1707.04249) with that on local continuity bounds (arXiv:1706.02212), and unifies the notation. Abstract: “Majorization is a pre-order of vectors, giving a sense in which one vector can be said to be more disordered than another. Two given vectors, however, may be incomparable. This concept has been extended