Extremal and Additive Combinatorial Aspects in Information Theory
A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".
Deadline for manuscript submissions: closed (15 September 2024) | Viewed by 13890
Special Issue Editor
2. Faculty of Mathematics, Technion—Israel Institute of Technology, Haifa 3200003, Israel
Interests: information theory; coding theory; probability theory; combinatorics
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
Extremal combinatorics deals with the problem of determining or bounding the maximum or minimum possible cardinality of a finite set of objects which satisfies certain requirements. Many interesting problems in extremal combinatorics are motivated by fundamental questions in information theory such as the Shannon capacity of graphs and its connection to Ramsey numbers and to perfect graphs, the zero-error capacity of communication channels, and Witsenhausen’s rate for graphs. The Shannon entropy and other classical information measures also serve as powerful tools in proving various extremal combinatorial and graph-theoretic results, such as Shearer’s lemma and its applications in extremal combinatorics and graph theory, the submodularity properties of information measures and their utility in the derivation of information inequalities and bounds in extremal graph theory, entropy-based proofs of combinatorial results such as Bregman’s theorem in matrix theory, Spencer’s theorem in discrepancy theory, problems related to intersection families in extremal set theory, and bounds for locally decodable codes.
Additive combinatorics (or arithmetic combinatorics) is a branch of mathematics which lies at the intersection of combinatorics, number theory, Fourier analysis, and ergodic theory. It has deep connections to information inequalities such as entropy inequalities for sums and differences of random variables with their relationship to probability limit theorems, and the adaptation of an information-theoretic approach for the study of sumset inequalities in additive combinatorics. Additionally, Szemeredi’s regularity lemma is a tool in graph theory that plays an important role in additive combinatorics; it was revisited by Tao from the perspective of information theory and probability theory, followed by a strengthening of this lemma.
It is the purpose of this Special Issue to explore recent developments in extremal and additive combinatorics from the perspective of information theory. Topics of interest include, but are not limited to:
- Information-theoretic proofs in extremal combinatorics;
- Zero-error information theory;
- Graph capacities and graph entropy;
- Graph-theoretic results by information-theoretic tools;
- Connections between extremal set theory and information theory;
- Multiuser problems for special channels, and their relation to extremal and additive combinatorics;
- Information inequalities and additive combinatorics;
- Applications of additive combinatorics in information theory problems.
Prof. Dr. Igal Sason
Guest Editor
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