In this paper, we observe the possibility that the group \(S_{n}\times S_{m}\) acts as a flag-tra... more In this paper, we observe the possibility that the group \(S_{n}\times S_{m}\) acts as a flag-transitive automorphism group of a block design with point set \(\{1,\ldots ,n\}\times \{1,\ldots ,m\},4\leq n\leq m\leq 70\). We prove the equivalence of that problem to the existence of an appropriately defined smaller flag-transitive incidence structure. By developing and applying several algorithms for the construction of the latter structure, we manage to solve the existence problem for the desired designs with \(nm\) points in the given range. In the vast majority of the cases with confirmed existence, we obtain all possible structures up to isomorphism.
In the paper, we consider the problem of determining a subset of the complex plane which contains... more In the paper, we consider the problem of determining a subset of the complex plane which contains all eigenvalues of the given complex matrix. We point to several applications of the gained eigenvalue inclusion sets in different branches of applied mathematics.
All primitive symmetric designs with at most 255 points have been constructed and classified (S. ... more All primitive symmetric designs with at most 255 points have been constructed and classified (S. Braic, PhD thesis, 2007). In this research we either prove the non-existence or give explicit construction of some symmetric designs with primitive automorphism groups of higher degree. The method of design construction is based on an automorphism group action, and on the theory of difference sets, multiplier theorems in particular. It involves programming and wide-range computations. We make use of software package GAP, the well-known system for computational group theory, and the library of primitive groups which it contains.
Acta mathematica Spalatensia. Series didactica, 2020
U ovom radu predstavit će se igra RasTpad, autora Krune Matića, te dati njena matematička analiza... more U ovom radu predstavit će se igra RasTpad, autora Krune Matića, te dati njena matematička analiza koja opisuje strategiju pronalaska rješenja igre i osnovni pristup analizi broja rješenja s obzirom na zadano početno stanje tablice igre.
In this paper, we observe the possibility that the group \(S_{n}\times S_{m}\) acts as a flag-tra... more In this paper, we observe the possibility that the group \(S_{n}\times S_{m}\) acts as a flag-transitive automorphism group of a block design with point set \(\{1,\ldots ,n\}\times \{1,\ldots ,m\},4\leq n\leq m\leq 70\). We prove the equivalence of that problem to the existence of an appropriately defined smaller flag-transitive incidence structure. By developing and applying several algorithms for the construction of the latter structure, we manage to solve the existence problem for the desired designs with \(nm\) points in the given range. In the vast majority of the cases with confirmed existence, we obtain all possible structures up to isomorphism.
In the paper, we consider the problem of determining a subset of the complex plane which contains... more In the paper, we consider the problem of determining a subset of the complex plane which contains all eigenvalues of the given complex matrix. We point to several applications of the gained eigenvalue inclusion sets in different branches of applied mathematics.
All primitive symmetric designs with at most 255 points have been constructed and classified (S. ... more All primitive symmetric designs with at most 255 points have been constructed and classified (S. Braic, PhD thesis, 2007). In this research we either prove the non-existence or give explicit construction of some symmetric designs with primitive automorphism groups of higher degree. The method of design construction is based on an automorphism group action, and on the theory of difference sets, multiplier theorems in particular. It involves programming and wide-range computations. We make use of software package GAP, the well-known system for computational group theory, and the library of primitive groups which it contains.
Acta mathematica Spalatensia. Series didactica, 2020
U ovom radu predstavit će se igra RasTpad, autora Krune Matića, te dati njena matematička analiza... more U ovom radu predstavit će se igra RasTpad, autora Krune Matića, te dati njena matematička analiza koja opisuje strategiju pronalaska rješenja igre i osnovni pristup analizi broja rješenja s obzirom na zadano početno stanje tablice igre.
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Papers by Joško Mandić