Chair:
Assoc. Prof. Vedrana Mikulić Crnković
Members:
- Prof. Dean Crnković
- Prof. Sanja Rukavina
- Assoc. Prof. Doris Dumičić Danilović
- Assoc. Prof. Marija Maksimović
- Assoc. Prof. Vedrana Mikulić Crnković
- Assoc. Prof. Andrea Švob
- Assist. Prof. Sara Ban Martinović
- Assist. Prof. Ana Grbac
- Assist. Prof. Daniel Hawtin
- Assist. Prof. Nina Mostarac
- Assist. Prof. Marina Šimac
- Dr. Nour Alnajjarine
- Dr. Matteo Mravić
- Dr. Ivona Traunkar
- Dr. Tin Zrinski
- Dr. Matea Zubović Žutolija
- Daniel Šanko
- Ana Šumberac
Research
Division of Discrete Mathematics was established in early 2011. The research activity of the Division’s members is in the area of combinatorial and discrete mathematics, in particular design theory, graph theory, and coding theory.
Active Research Projects
- Designs, graphs and codes (project leader: Dean Crnković) IP-HRZZ project, Croatian Science Foundation (2023-2027)
- Codes, group actions, representations and geometry (project leader: Daniel Hawtin), Institutional project of University of Rijeka, (2025-2029)
- Interdisciplinary approach to teaching and promotiong mathematics (project leader: Vedrana Mikulić Crnković), Institutional project of University of Rijeka, (2025-2029)
- Finite geometries, graphs and groups (project leader: Andrea Švob), Institutional project of University of Rijeka, (2025-2029)
- Distance-regularized graphs, Terwiliger algebras, codes and combinatorial structures, project leaders: Marija Maksimović (University of Rijeka, Faculty of Mathematics), Blas Fernandez (University of Primorska, Faculty of Mathematics, Natural Sciences and Information Technologies), Bilateral project with Slovenia, (2025-2026)
- Directed graphs in commutative association schemes and associated codes (project leaders: Vedrana Mikulić Crnković (University of Rijeka, Faculty of Mathematics), Safet Penjić (University of Primorska, Faculty of Mathematics, Natural Sciences and Information Technologies), Bilateral project with Slovenia, (2025-2026)
Finished Research Projects
- Galois geometry and coherent configurations (project leader: Andrea Švob) UIP-HRZZ project, Croatian Science Foundation, (2021-2025)
- Combinatorial designs and related structures (project leader: Dean Crnković) Uniri project, (2024-2025)
- Finite geometries and groups (project leader: Andrea Švob) Uniri project, (2024-2025)
- Properties and methods of construction of distance-biregular graphs and Z_2k codes (project leader: Sanja Rukavina) Uniri project, (2024-2025)
- Constructions of digraphs and related linear codes, (project leader: Vedrana Mikulić Crnković) Uniri project, (2024-2025)
- Algebraic symmetry of q-analogs of graphs (project leader: Daniel Hawtin) Uniri project, (2024-2025)
- Certain algebraic aspects of various incidence structures, project leaders: Sanja Rukavina (University of Rijeka, Faculty of Mathematics); Štefko Miklavič (Univerza na Primorskem, Institut Andrej Marušič), Bilateral project with Slovenia, (2023-2024)
- Synergistic applications of new methods from design theory, configurations, graph theory, and group theory, project leaders: Andrea Švob (University of Rijeka, Faculty of Mathematics); Tomaž Pisanski (University of Primorska, Faculty of Mathematics, Natural Sciences and Information Technologies), Bilateral project with Slovenia, (2023-2024)
- Codes, groups and combinatorial structures (project leader: Dean Crnković) Uniri project, (2018-2023)
- Designs, graphs and linear codes (project leader: Sanja Rukavina) Uniri project, (2018-2023)
- Permutation groups as designs, geometric designs, codes and finite geometries (project leader: Vedrana Mikulić Crnković) Uniri project, (2018-2023)
- Combinatorial Objects and Codes (project leader: Dean Crnković) IP-HRZZ project, Croatian Science Foundation, (2019-2022)
- Codes, their preservers, and corresponding incidence structure, project leaders: Vedrana Mikulić (University of Rijeka, Faculty of Mathematics), Marko Orel (Univerza na Primorskem, Inštitut Andrej Marušič), Bilateral project with Slovenia, (2020-2022)
- Designs, codes, graphs and cryptography – an interdisciplinary approach in analysis of certain discrete structures project leaders: Sanja Rukavina (University of Rijeka, Faculty of Mathematics), Enes Pašalić (Univerza na Primorskem, Inštitut Andrej Marušič), Bilateral project with Slovenia, (2018-2019)
- Codes and Related Combinatorial Structures (project leader: Dean Crnković) IP-HRZZ project, Croatian Science Foundation, (2014-2018)
- Block designs, strongly regular graphs, and related combinatorial structures (project leader: Dean Crnković) Uniri project, (2013-2018)
- Permutation groups as designs, geometric designs, codes and finite geometries (project leader: Vedrana Mikulić Crnković), Uniri project for young researchers (2017)
- Block designs, strongly regular graphs, and related combinatorial structures (project leader: prof. dr. sc. Dean Crnković) financed by Ministry of Science, Education and Sports of Republic of Croatia, (2007-2013)
It should be noted that in 2010, Division members participated in the organisation of the NATO Advanced Study Institute on Information Security and Related Combinatorics summer school. Furthermore, in 2021 the conference Combinatorial Designs and Codes was organised as a satellite event of the 8th European Congress of Mathematics, and in 2023 the conference Rijeka Conference on Combinatorial Objects and Their Applications was organised. 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 Research Papers
- M. Shi, R. Liu, D. Crnković, P. Solé, A. Švob, Ternary isodual codes and 3-designs, Des. Codes Cryptogr. 93 (2025), 1671-1685.
- D. Crnković, M. De Boeck, F. Pavese, A. Švob, q-Analogs of divisible design graphs and Deza graphs, J. Combin. Theory Ser. A 216 (2025), 106047, 18 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, LCD subspace codes, Des. Codes Cryptogr. 91 (2023), 3215-3226.
- D. Crnković, A. Švob, Tolerance fuzzy graphs, J. Intell. Fuzzy Systems 45 (2023), 4023–4029.
- M. Shi, Y. Li, W. Cheng, D. Crnković, D. Krotov, P. Solé, Self-dual bent sequences for complex Hadamard matrices, Des. Codes Cryptogr. 91 (2023), 1453-1474.
- V. Mikulić Crnković, I. Traunkar, Self-orthogonal codes constructed from weakly self-orthogonal designs invariant under an action of M11, Appl. Algebra Eng. Commun. Comput. 34 (2023), 139-156.
- R. F. Bailey, D. R. Hawtin, On the classification of binary completely transitive codes with almost-simple top-group, European J. Combin. 107 (2023), 103604, 28 pp.
- D. R. Hawtin, J. Lansdown, The non-existence of block-transitive subspace designs, Combinatorial Theory 2, No. 1 (2022), Paper No. 11, 13 pp.
- D. Crnković, A. Švob, Switching for 2-designs, Des. Codes Cryptogr. 90 (2022), 1585-1593.
- D. Crnković, D. R. Hawtin, A. Švob, Neighbour-transitive codes and partial spreads in generalised quadrangles, Des. Codes Cryptogr. 90 (2022), 1521-1533.
- D. Crnković, T. Zrinski, Constructing block designs with a prescribed automorphism group using genetic algorithm, J. Combin. Des. 30 (2022), 515-526.
- D. Crnković, S. Rukavina, M. Šimac, LDPC codes from cubic semisymmetric graphs, Ars Math. Contemp. 22 (2022), #P2.03, 13 pages.
- D. Crnković, D. Dumičić Danilović, R. Egan, A. Švob, Periodic Golay pairs and pairwise balanced designs, J. Algebraic Combin. 55 (2022), 245-257.
- D. Crnković, S. Rukavina, A. Švob, Self-orthogonal codes from equitable partitions of association schemes, J. Algebraic Combin. 55 (2022), 157-171.
- D. Crnković, A. Švob, New symmetric 2-(176,50,14) designs, Discrete Math. 344 (2021), 112623, 3 pages.
- D. R. Hawtin, s-Elusive codes in Hamming graphs, Des. Codes Cryptogr. 89 (2021), 1211–1220.
- D. Crnković, D. Dumičić Danilović, S. Rukavina, On automorphism groups of a biplane (121,16,2), Discrete Math. 344 (2021), 112508, 8 pages.
- R. F. Bailey, D. R. Hawtin, On the 486-vertex distance-regular graphs of Koolen-Riebeek and Soicher, Electron. J. Combin. 27 (2020), #P3.13, 12 pages.
- D. Crnković, N. Mostarac, B. G. Rodrigues, L. Storme, s-PD-sets for codes from projective planes PG(2,2^h), 5 ≤ h ≤ 9, Adv. Math. Commun. 15 (2021), 423-440.
- D. Crnković, A. Švob, V. D. Tonchev, Strongly regular graphs with parameters (81,30,9,12) and a new partial geometry, J. Algebraic Combin. 53 (2021), 253-261.
- D. Crnković, R. Egan, A. Švob, Self-orthogonal codes from orbit matrices of Seidel and Laplacian matrices of strongly regular graphs, Adv. Math. Commun. 14 (2020), 591-602.
- D. Crnković, H. Kharaghani, A. Švob, Divisible design Cayley digraphs, Discrete Math. 343 (2020), 111784, 8 pages.
- D. Crnković, R. Egan, A. Švob, Constructing self-orthogonal and Hermitian self-orthogonal codes via weighing matrices and orbit matrices, Finite Fields Appl. 55 (2019), 64-77.
- M. De Boeck, M. Rodgers, L. Storme, A. Švob, Cameron-Liebler sets of generators in finite classical polar spaces, J. Combin. Theory Ser. A 167 (2019), 340-388.
- D. Crnković, N. Mostarac, Self-dual codes from orbit matrices and quotient matrices of combinatorial designs, Discrete Math. 341 (2018), 3331–3343.
- D. Crnković, S. Rukavina, A. Švob, New strongly regular graphs from orthogonal groups O+(6,2) and O-(6,2), Discrete Math. 341 (2018), 2723-2728.
- D. Crnković, V. Mikulić Crnković, B. G. Rodrigues, On self-orthogonal designs and codes related to Held’s simple group, Adv. Math. Commun. 12 (2018), 607-628.
- D. Crnković, R. Egan, A. Švob, Orbit matrices of Hadamard matrices and related codes, Discrete Math. 341 (2018), 1199-1209.
Members of the Division participate in the implementation of the Doctoral Program in Mathematics (joint program of J. J. Strossmayer University of Osijek, University of Rijeka, University of Split, University of Zagreb) organizing Finite Mathematics Seminar. As a part of the Seminar, members of the Division present their own research work as well as other relevant articles in the area of research.
We point out that Andrea Švob received the University of Rijeka Foundation Award for the calendar year 2024, in the category of scientists – biomedical and natural sciences, and the University of Rijeka Foundation Award for the calendar year 2015, in the category of young scientists – natural and technical sciences. The University of Rijeka Foundation Award for the academic year 2008/2009, in the category of young scientists – natural and technical sciences, was also received by Vedrana Mikulić Crnković, who is also a recipient of the State Award for Science for 2020 in the category of promotion of science.
Teaching
Members of the Division of Discrete Mathematics participate in the delivery of courses within the study programmes of the Faculty of Mathematics, as well as teaching mathematics courses in study programmes led by other faculties at University of Rijeka. Together and in collaboration with other faculty staff, they work on designing and delivering each individual course with the aim of improving the quality of study programmes and strengthening the connections between courses.
Division members use the Laboratory for Discrete Mathematics for their scientific work. The laboratory is also used for teaching in the graduate study programme Discrete Mathematics and Applications.
Two Division members received an award for special contribution to the development of e-learning at the University of Rijeka. One for the course Applications of Computers in Mathematics (academic year 2009/2010) and another for the course Models of Geometry (academic year 2010/2011). Furthermore, Division staff have received the University of Rijeka Teaching Excellence Award: Ivona Novak and Andrea Švob for the academic year 2015/2016, Sanja Rukavina and Marina Šimac for the academic year 2017/2018, Nina Mostarac and Andrea Švob for the academic year 2019/2020, Tin Zrinski for the academic year 2022/2023, Matea Zubović Žutolija for the academic year 2023/2024, Daniel Šanko for the academic year 2024/2025, and Ana Šumberac for the academic year 2025/2026.
Division members are authors and presenters of numerous popular lectures and workshops delivered to primary and secondary school students with the aim of promoting mathematics and mathematics studies, and actively participate in many professional projects and in the work of numerous associations such as the Society of Mathematicians and Physicists, the MatRi Alumni Club, Zlatni rez, Universitas, and the Centre for Technical Culture Rijeka.
Vedrana Mikulić Crnković leads two professional projects: Erasmus+ projekt SciMaG (1 September 2023 – 31 August 2026) i Erasmus+ projekt InAMath (1 September 2020 – 28 February 2023).