Research interests

My research interests include topics in pure math, including algebraic combinatorics, partition theory and theoretical physics.

Contact

University of Zagreb, Faculty of Science

Bijenička c. 32, HR-10000 Zagreb, Croatia

E-mail: imartinjak@phy.hr

Recent Publications

(with R. Škrekovski)* Lah Numbers and Lindstrőm’s lemma*, Comptes Rendus Mathematique, 356(1), 2018, 5-7

We provide a combinatorial interpretation of Lah numbers by means of planar networks. Henceforth, as a conesquence of Lindstrőm’s lemma, we conclude that the related Lah matrix possesses a remarkable property of total non-negativity.

* Two infinite families of terminating binomial sums, *Period Math Hung, 75(2), 2017, 244-254

* Algebraic Properties of the Canonical Incidence Matrix of a Biplane, *Discrete Math, 340/12, 2017, 2807-2812

* Two Extensions of the Sury’s Identity*, Amer. Math. Monthly, 123 (9), 2016, p.919.

(with D. Svrtan)* Some Families of Identities for the Integer Partition Function*, Math. Commun., 20(2), 2015, 193-200.

Recent Talks and Seminars

*“Enumeration of some families of lattice paths – bijective proofs”, seminar*, Department of Mathematics, University of Zagreb, 2017 abstract, photo.

*“Something new of MacMahon’s theorem on plane partitions”, seminar*, Department of Mathematics, University of Zagreb, 2017 abstract.

*“Symmetric Association Schemes and Finite Geometries” *, 20th Scientific-Professional Colloquium on Geometry and Graphics, Fužine, 2017 abstract.

*(with K. Rožman) “Oscilacijske matrice modela na rešetki i hipermersennovih nizova”, 10. ZS Hrvatskog fizikalnog društva Baška, Hrvatska, 2017, poster presentation abstract (cro). *

*“Slutnje o Durfeevim matricama i ekstenzijama MacMachonovog teorema” *, Workshop in graph theory and applications, University of Mostar, 2017 abstract (cro), in media

Further links

Seminar in Combinatorics and Discrete Mathematics

My publications on arXiv

My publications on Croatian Scientific Bibliography