Download or read book Collected Results on Semigroups, Graphs and Codes written by Albert Vico Oton and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we present a compendium of five works where discrete mathematics play a key role. The first three works describe diferent developments and applications of the semigroup theory while the other two have more independent topics. First we present a result on semigroups and code eficiency, where we introduce our results on the so-called Geil-Matsumoto bound and Lewittes' bound for algebraic geometry codes. Following that, we work on semigroup ideals and their relation with the Feng-Rao numbers; those numbers, in turn, are used to describe the Hamming weights which are used in a broad spectrum of applications, i.e. the wire-tap channel of type II or in the t-resilient functions used in cryptography. The third work presented describes the non-homogeneous patterns for semigroups, explains three diferent scenarios where these patterns arise and gives some results on their admissibility. The last two works are not as related as the first three but still use discrete mathematics. One of them is a work on the applications of coding theory to fingerprinting, where we give results on the traitor tracing problem and we bound the number of colluders in a colluder set trying to hack a fingerprinting mark made with a Reed-Solomon code. And finally in the last work we present our results on scientometrics and graphs, modeling the scientific community as a cocitation graph, where nodes represent authors and two nodes are connected if there is a paper citing both authors simultaneously. We use it to present three new indices to evaluate an author's impact in the community.