## Division of Discrete Mathematics

Chair:

Assist. Prof. Vedrana Mikulić Crnković

Members:

- Prof. Dean Crnković
- Prof. Sanja Rukavina
- Assist. Prof. Vedrana Mikulić Crnković
- Assist. Prof. Andrea Švob
- Dr. Doris Dumičić Danilović
- Dr. Ronan Egan
- Dr. Marija Maksimović
- Dr. Nina Mostarac
- Dr. Marina Šimac
- Sara Ban
- Ana Grbac
- Matteo Mravić
- Ivona Novak
- Tin Zrinski
- Matea Zubović

Division of Discrete Mathematics was formed in early 2011. The discrete mathematics research group works in the field of combinatorics and discrete mathematics, including finite groups, finite geometries, design theory, graph theory, as well as coding theory and cryptography with applications.

Division of Discrete Mathematics was formed in early 2011.

Active projects:

- Codes and Related Combinatorial Structures (principal investigator: Dean Crnković) funded by the Croatian Science Foundation
- Block designs, strongly regular graphs and related combinatorial structures (principal investigator: Dean Crnković), support for research at the University of Rijeka
- Permutation groups as designs, geometrical designs, codes and finite geometries (principal investigator: Vedrana Mikulić Crnković), initial support for research at the University of Rijeka
- Designs, codes, graphs and cryptography - interdisciplinary approach to discrete structure analysis (principal investigator: Sanja Rukavina), bilateral project Načrti, kode, grafi in kriptografija interdisciplinarni pristop v analizi določenih diskretnih struktur (Univerza na Primorskem, Inštitut Andrej Marušič - principal investigator Enes Pasalic).

Members of the Division were, from 2007 to 2013, actively participating in the project Block designs, strongly regular graphs and related combinatorial structures (principal investigator: prof. Dean Crnković) funded by the Ministry of Science, Education and Sports of the Republic of Croatian.

Members of the Division in 2010 participated in the organization of NATO Advanced Study Institute on Information Security and Related Combinatorics summer school (main sponsor: NATO; Organizing Committee: Dean Crnkovic; Willem Haemers, Tilburg University; Sanja Rukavina, Vladimir D. Tonchev, Michigan technological University).

Members of the Division are actively involved in the international scientific community, collaborating with mathematicians from different countries and participating at international scientific conferences.

Selected activities:

- D. Crnković, S. Rukavina, L. Simčić, On triplanes of order twelve admitting an automorphism of order six and their binary and ternary codes, Util. Math., 103 (2017), 23-40.
- R. Egan, D. L. Flannery, Automorphisms of generalized Sylvester matrices, Discrete Math. 340 (2017), 516-523.
- M. De Boeck, L. Storme, A. Švob, The Cameron-Liebler problem for sets, Discrete Math. 339 (2016), 470-474.
- D. Crnković, S. Rukavina, Self-dual codes from extended orbit matrices of symmetric designs, Des. Codes Cryptogr. 79 (2016), 113-120.
- D. Crnković, N. Mostarac, S. Rukavina, Self-dual codes from quotient matrices of symmetric divisible designs with the dual property, Discrete Math. 339 (2016), 409-414.
- D. Crnković, D. Dumičić Danilović, Finding unitals in symmetric designs using a modified genetic algorithm, Math. Pannon., 24 (2014), 183-196.
- D. Crnković, W. H. Haemers, Walk-regular divisible design graphs, Des. Codes Cryptogr., 72 (2014), 165-175.
- D. Crnković, Classes of self-orthogonal or self-dual codes from orbit matrices of Menon designs, Discrete Math., 327 (2014), 91-95.
- D. Crnković, V. Mikulić Crnković, A. Švob, On some transitive combinatorial structures constructed from the unitary group U(3,3), J. Statist. Plann. Inference 144 (2014), 19-40.
- D. Crnković, V. Mikulić, Unitals, projective planes and other combinatorial structures constructed from the unitary groups U(3,q), q=3,4,5,7, Ars Combin. 110 (2013), 3--13.
- D. Crnković, V. Mikulić Crnković, B. G. Rodrigues, Some optimal codes and strongly regular graphs from the linear group L4(3), Util. Math. 89 (2012), 237--255.
- D. Crnković, B. G. Rodrigues, S. Rukavina, L. Simčić, Ternary codes from the strongly regular (45,12,3,3) graphs and orbit matrices of 2-(45,12,3) designs, Discrete Math. 312 (2012), 3000-3010.
- Information Security, Coding Theory and Related Combinatorics / Crnković, Dean; Tonchev, Vladimir (ur.). Amsterdam : IOS Press, 2011 (urednička knjiga).
- D. Crnković, A Series of Siamese Twin Designs, Discrete Math. 309 (2009), 322-327.
- D. Crnković, A series of Menon designs and 1-rotational designs, Finite Fields Appl. 13, No. 4 (2007), 1001-1005.
- D. Crnković, A Series of Regular Hadamard Matrices, Des. Codes Cryptogr. 39, No. 2 (2006), 247-251.
- D. Crnković, S. Rukavina, M. Schmidt, A Classification of all Symmetric Block Designs of Order Nine with an Automorphism of Order Six, J. Combin. Des. 14, No. 4 (2006), 301-312.
- D. Crnković, S. Rukavina, Construction of Block Designs Admitting an Abelian Automorphism Group, Metrika 62, No. 2-3 (2005), 175-183