UNIRI projekt 2024 | UNIRI project 2024

Konačne geometrije i grupe

Finite geometries and groups

Osnovni cilj ovog projekta je dati značajan doprinos raznim granama matematike u području diskretne i kombinatorne matematike, posebno proučavanju konačnih geometrija i grupa i s njima povezanih konačnih incidencijskih struktura. Osnovna i glavna tema ovog projekta je konstrukcija kombinatoričkih struktura baziranih na konačnim geometrijama i konstrukcijama struktura iz konačnih grupa. Konstruirat ćemo, analizirati i opisati strukture koje su dobivene iz konačnih grupa, posebno geometrijskih grupa za čiju konstrukciju je potrebno široko znanje iz konačnih geometrija. Projekt će se najviše baviti interakcijom između konačnih geometrija i kombinatoričkih struktura te njihovom vezom s konačnim grupama.

The main objective of this project is to make significant contributions to several different areas of mathematics in the field of discrete and combinatorial mathematics, especially to the studies of finite geometry and coherent configurations and finite incidence structures connected with them. The main topic of the proposed research is a construction of combinatorial structures arrising from finite geometry and from finite groups. We will construct, analyse and describe structures obtained from finite groups, especially geometrical groups for which deep study in finite geometry is crucial. The project will mostly deal with the interplay between finite geometry and combinatorial structures and their connection to coherent configurations.

Voditelj / Principal investigator:
izv. prof. dr. sc. Andrea Švob

e-mail: asvob@math.uniri.hr

(Fakultet za matematiku, Sveučilište u Rijeci / Faculty of Mathematics, University of Rijeka)

Istraživački tim / Research team:
doc. dr. sc. Nina Mostarac

(Fakultet za matematiku, Sveučilište u Rijeci / Faculty of Mathematics, University of Rijeka)

dr. sc. Tin Zrinski

(Fakultet za matematiku, Sveučilište u Rijeci / Faculty of Mathematics, University of Rijeka)

Ana Šumberac

(Fakultet za matematiku, Sveučilište u Rijeci / Faculty of Mathematics, University of Rijeka)

Objavljeni radovi / Published works:
D. Dumičić Danilović, A. Švob, On Hadamard 2-(51, 25, 12) and 2-(59, 29, 14) designs, AIMS Math. 9 (2024), 23047-23059. doi: 10.3934/math.20241120
A. E. Brouwer, D. Crnković, A. Švob, A construction of directed strongly regular graphs with parameters (63,11,8,1,2), Discrete Math. 347 (2024), 114146, 3 pages.
M. Braun, D. Crnković, M. De Boeck, V. Mikulić Crnković, A. Švob, q-Analogs of strongly regular graphs, Linear Algebra Appl. 693 (2024), 362-373.
D. Crnković, A. Švob, Self-Orthogonal Codes from Deza Graphs, Normally Regular Digraphs and Deza Digraphs, Graphs Combin. (2024), 40:35, 12 pages.
D. Crnković, S. Rukavina, A. Švob, Self-orthogonal codes from equitable partitions of distance-regular graphs, Adv. Math. Commun. 18 (2024), 651-660.
Pozvana predavanja / Invited talks:
Andrea Švob, Some constructions of strongly regular graphs and digraphs, Combinatorial Designs and Codes (CODESCO24), Sevilla, Spain, July 8-12, 2024.
Andrea Švob, Doubly even self-dual codes and even unimodular lattices constructed from Hadamard matrices, 8th Croatian Mathematical Congress, Osijek, Croatia, July 2-5, 2024.
Izlaganja na konferencijama / Talks:
Nina Mostarac, LDPC LCD codes from odd graphs, 8th Croatian Mathematical Congress, Osijek, Croatia, July 2-5, 2024.
Ana Šumberac, Doubly even self-orthogonal codes from incidence and orbit matrices of quasi-symmetric designs, 8th Croatian Mathematical Congress, Osijek, Croatia, July 2-5, 2024.
Tin Zrinski, Genetic algorithms for construction of SRGs and DSRGs from orbit matrices, 8th Croatian Mathematical Congress, Osijek, Croatia, July 2-5, 2024.
Andrea Švob, Doubly even self-dual codes constructed from Hadamard matrices Combinatorics 2024, Riva Marina Resort, Carovigno (Br), Italy, 3-7 June 2024.
Tin Zrinski, Applications of genetic algorithms for constructions of SRGs and DSRGs, Combinatorial Constructions Conference (CCC), Dubrovnik, Croatia, April 7-13, 2024.
Andrea Švob, On some structures related to intriguing sets of strongly regular graphs, Combinatorial Constructions Conference (CCC), Dubrovnik, Croatia, April 7-13, 2024.

Članovi istraživačkog tima izlažu o svojim rezultatima i u okviru Seminara za konačnu matematiku .