Inequalities Revisited.

Abstract: In the past over two decades, researchers in information theory have obtained very fruitful results in the study of the Shannon entropy. This study has led to the discovery of a new class of constraints on the Shannon entropy, called non-Shannon-type inequalities. Intimate connections between the Shannon entropy and different branches of mathematics including finite group theory, combinatorics, Kolmogorov complexity, probability, matrix theory, etc, have been established. All these discoveries are based on a geometrical interpretation of constraints on the entropy function. We assert that the same formality can be applied to the study of inequalities in other branches of mathematics. To illustrate the idea, we revisit with this formality a few celebrated inequalities: the AM—GM inequality, the Markov inequality, and the Cauchy—Schwarz inequality. Applications of this formality has the potential of leading to the discovery of new inequalities in different branches of mathematics.

Computer scienceMathematics

Audience: researchers in the discipline

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Seminar on Algorithmic Aspects of Information Theory

Series comments: This online seminar is a follow up of the Dagstuhl Seminar 22301, www.dagstuhl.de/en/program/calendar/semhp/?semnr=22301.