Supervisor: doc. RNDr. Tatiana Jajcayova, PhD.

Student: Erik Szalay

Aim: The main topic of this project is a part of the combinatorial number theory. We will study generalized difference sets on subsets of positive integers whose differences include each positive integer with a prescribed number of repetitions. The twofold aim of the project is to approach the classification of admissible repetition sequences of finite generalized difference sets and the design of algorithms that produce generalized difference sets with additional properties for specified admissible sequences. The part of the project is to program and analyse developed algorithms.

30.10.2018: Thesis web page

13.11.2018: Thesis timeline

13.11.2018: Application for testing properties of sequences, testing of small sequences

27.11.2018: Finalization of collecting and studying sources

12.1.2019: Writing up theoretical context and background and designing prototype of software tools

31.1.2019: Testing of medium sequences, optimization of approximation

31.3.2019: Testing of large sequences, optimization of approximation, sequence generation

30.4.2019: First version of Thesis

15.5.2019: Finalization of Thesis

First Chapter of the Bachelor’s Thesis and Prototype

Tatiana B. Jajcayová: Generalized Difference Sets

Swara Kopparty: Results on Frequency Sequences

J. H. van Lint, R. M. Wilson: A Course in Combinatorics, 2nd edition

Cambridge University Press 2001

ISBN-13 978-0-511-67289-7

Emily H. Moore , Harriet S. Pollatsek: Difference Sets: Connecting Algebra, Combinatorics, and Geometry

American Mathematical Society, 2013

ISBN-13: 978-0821891766

Bachelor’s Thesis, 2014

Study programme: Applied Computer Science

Field of study: 9.2.9 Applied Informatics

Department: Department of Applied Informatics

Supervisor: RNDr. Tatiana Jajcayová

Ivana Kellyérová: Generalized difference sets

Bachelor’s Thesis, 2014

Study programme: Applied Computer Science

Field of study: 2511 Applied Informatics

Department: Department of Applied Informatics

Supervisor: RNDr. Tatiana Jajcayová

Bc. Marián Opial: Generalized difference sets – An Algorithmic Approach

Master’s Thesis, 2017

Study programme: Applied Computer Science

Field of study: 2511 Applied Informatics

Department: Department of Applied Informatics

Supervisor: RNDr. Tatiana Jajcayová Presentation

3/18/2019 - Wrote a chapter about a different way to think about Generalized Difference Sets; that there exists an isomorphism between the sets and complete undirected weighted graphs, which satisfy a specific condition.

4/2/2019 - Wrote a chapter describing the conditions that eliminate wrong sequences that I discovered with proofs.