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
Science
Division of Discrete Mathematics was formed in early 2011. The division consists of 17 members, nine of which are holding tenure track positions, five senior teaching assistants and three teaching assistants.
Scientific work of the members of the Division is in the area of combinatorics and discrete mathematics, especially design theory, graph theory and coding theory.
Active Research Projects
- Galois geometry and coherent configurations (project leader: Assoc. Prof. Andrea Švob), Croatian Science Foundation
- Neki algebarski aspekti različitih incidencijskih struktura (Nekateri algebraični vidiki raznih incidenčnih struktur), project leaders: Prof. Sanja Rukavina (University of Rijeka, Faculty of Mathematics); Prof. Štefko Miklavič (Univerza na Primorskem, Institut Andrej Marušič), 2023 – 2024
- Sinergijske primjene novih metoda iz teorije dizajna, konfiguracija, grafova i grupa (Sinergetske aplikacije novejših metod iz teorije načrtov, konfiguracij, grafov in grup), project leaders: Assoc. Prof. Andrea Švob (University of Rijeka, Faculty of Mathematics); Prof. Tomaž Pisanski (Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije), 2023 – 2024
- Kodovi, grupe i kombinatoričke strukture (project leader: Prof. Dean Crnković), Research Support of the University of Rijeka
- Dizajni, grafovi i linearni kodovi (project leader: Prof. Sanja Rukavina), Research Support of the University of Rijeka
- Permutacijske grupe kao dizajni, geometrijski dizajni i konačne geometrije (project leader: Assoc. Prof. Vedrana Mikulić Crnković), Research Support of the University of Rijeka
Finished Research Projects
- Combinatorial Objects and Codes (project leader: Prof. Dean Crnković), Croatian Science Foundation, 2019 – 2020
- Kodovi, njihovi konzervatori i pripadne incidencijske strukture (Kode, njihovi ohranjevalci in pripadajoče incidenčne strukture), project leaders: Assoc. Prof. Vedrana Mikulić Crnković Sveučilište u Rijeci, Department of Mathematics, University of Rijeka; Prof. Marko Orel Univerza na Primorskem, Institut Andrej Marušič, 2020 – 2022
- Dizajni, kodovi, grafovi i kriptografija – interdisciplinarni pristup analizi diskretnih struktura (project leader: Sanja Rukavina), bliateral project Načrti, kode, grafi in kriptografija interdisciplinarni pristop v analizi določenih diskretnih struktur (Univerza na Primorskem, Inštitut Andrej Marušič – project leader: Prof. Enes Pašalić), 2018 – 2019
- Codes and Related Combinatorial Structures (project leader: Prof. Dean Crnković), Croatian Science Foundation, 2014 – 2018
- Blok dizajni, jako regularni grafovi i srodne kombinatoričke strukture (project leader: Prof. Dean Crnković), Research Support of the University of Rijeka, 2014 – 2018
- Permutacijske grupe kao dizajni, geometrijski dizajni, kodovi i konačne geometrije (project leader: Assoc. Prof. Vedrana Mikulić Crnković), Initial Research Support Programme of the University of Rijeka for Early-Career Researchers (2017)
- Blok dizajni, jako regularni grafovi i srodne kombinatoričke strukture (project leader: Prof. Dean Crnković) funded by the Ministry of Science, Education and Sports of the Republic of Croatia, 2007 – 2013.
In 2010, members of the Division participated in the organization of NATO Advanced Study Institute on Information Security and Related Combinatorics summer school (main sponsor: NATO; Organizing Committee: Dean Crnković; Willem Haemers, Tilburg University; Sanja Rukavina, Vladimir D. Tonchev, Michigan technological University).
We are especially proud that the article Self-dual codes from quotient matrices of symmetric divisible designs with the dual property (D. Crnković, N. Mostarac, S. Rukavina) is in the list of articles Editors’ Choice from Discrete Mathematics.
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
- 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 Croatian 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 has won the University of Rijeka Foundation Award for year 2015 in the category young scientists – natural and technical sciences and that Vedrana Mikulić Crnković was awarded the same for the academic year 2008/2009. Vedrana Mikulić Crnković has also received the Croatian National Award for Science (in the category of Science Promotion) for the year 2020.
Teaching
Since the academic year 2011/2012 the Division has been organizing and running graduate studies Discrete Mathematics and Its Applications. Members of the Division have designed and run courses in the area of discrete and combinatorial mathematics in these studies and work together on designing and running each course for the purpose of improving the quality of the studies and greater correlation between the courses. The Division is the executor of the project within which e-materials have been made for the course Introduction to Design Theory which has been financed by University of Rijeka (through the Tender for financing the development of e-courses in the academic year 2011/2012).
In 2012, the Laboratory for Discrete Mathematics was formed and equipped (with GAP and Magma software) and has since been used for research work by the members of the Division and for teaching purposes of the graduate studies Discrete Mathematics and Its Applications.
We point out that the members of the Division are course executors of two courses that have been awarded for special contribution for development of e-learning at the University of Rijeka: course ICT in Mathematics (academic year 2009/2010) and course Geometry (academic year 2010/2011). Furthermore, four members of the Division have won the University of Rijeka Teaching Excellence Award (Ivona Novak and Andrea Švob in academic year 2015/2016 and Sanja Rukavina and Marina Šimac in academic year 2017/2018).
Members of the Division are authors and executors of multiple popular lectures and workshops which are designed for the elementary and high school audiences for the purpose of popularization of mathematics and mathematical studies. They also actively participate in the work of associations such a as: Mathematicians and Physicists Society, Alumni Club MatRI, Zlatni rez, Universitas,…