### About P1-0285

Program Title: Algebra, Discrete Mathematics, Probability and Game Theory.

Program PI: Dragan Marušič.

Program Code: P1-0285.

Funding Organization: Slovenian Research Agency (ARRS).

Research Field (ARRS):

- 1.01.00 - Natural Sciences and Mathematics / Mathematics
- 1.07.00 - Natural Sciences and Mathematics / Computer Intensive Methods and Applications

Duration: 1. 1. 1999 - 31. 12. 2021.

Program Category: B.

Yearly Range: 2.69 FTE.

Sicris Profile of the program is avaliable here.

Abstract:

The research program is a continuation of the existing research program Algebra, discrete mathematics, probability and game theory (P1-0285), lead by Dragan Marušič. It includes the following organizations: the University of Primorska, the Institute of Mathematics, Physics and Mechanics, and the University of Nova Gorica.

The research program is of intra- and inter-disciplinary nature. Namely, it combines different parts of the following areas of mathematics: algebra, combinatorics with graph theory (discrete mathematics), probability, mathematical modeling and game theory with computer simulations. The program follows research goals pertaining to different fields. At the same time it creates a space for interaction of mathematicians within the Ljubljana-Koper-Nova Gorica triangle, thus contributing to the development of the university environment in the Primorska region.

Combinatorial language can often provide useful insights when studying structural properties of certain algebraic objects such as permutation groups. Conversely, when investigating structural properties of combinatorial objects admitting transitive group actions (or possibly intransitive actions with a small number of orbits), one often relies on purely algebraic results. An example of such a fruitful interplay is the main topic of the program, which draws together open questions from combinatorics and algebra: groups acting on graphs, structural properties of graphs with prescribed symmetry, graph covers, blocks of imprimitivity, algebraic aspects, Schur rings and coherent configurations, etc. In addition, interactions of combinatorics and algebra with other mathematical disciplines as well as its applications in other sciences, mathematical biology, probability and game theory are studied.

The research program group has been publishing its main results in prestigious international specialized journals. Recently, the group has started to disseminate the results also in highly ranked scientific general journals such as Journal of the European Math. Society, Transactions of the American Math. Society, and Science.

In the course of the last few years the research program group hosted many leading world experts, mostly as short term visits, but some of them also for a longer period. In the future the group will try to attract even more renowned visitors as well as postdoctoral researchers, and will continue to be active in organizing international scientific meetings with distinguished participants (see http://www.famnit.upr.si/en/conferences/).

The international importance of the results obtained by the members of the group and the goals of the program are well reflected in the number of publications in prestigious SCI journals and the number of pure WoS citations.