2011/08/18 by Khodakhast Bibak, Bibak, Khodakhast
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #Number Theory (math.NT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1108.3790
openalex publication_date 2011/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, additive combinatorics has blossomed into a vibrant area in\nmathematical sciences. But it seems to be a difficult area to define - perhaps\nbecause of a blend of ideas and techniques from several seemingly unrelated\ncontexts which are used there. One might say that additive combinatorics is a\nbranch of mathematics concerning the study of combinatorial properties of\nalgebraic objects, for instance, Abelian groups, rings, or fields. This\nemerging field has seen tremendous advances over the last few years, and has\nrecently become a focus of attention among both mathematicians and computer\nscientists. This fascinating area has been enriched by its formidable links to\ncombinatorics, number theory, harmonic analysis, ergodic theory, and some other\nbranches; all deeply cross-fertilize each other, holding great promise for all\nof them! In this exposition, we attempt to provide an overview of some\nbreakthroughs in this field, together with a number of seminal applications to\nsundry parts of mathematics and some other disciplines, with emphasis on\ncomputer science and cryptography.\n