Joško Mandić - Profile on Academia.edu (original) (raw)

Papers by Joško Mandić

Flag-transitive and point-imprimitive symmetric designs with λ ≤ 10

Journal of Combinatorial Theory, Series A, 2022

$Research paper thumbnail of Groups $S_n \times S_m$ in construction of flag-transitive block designs$

Glasnik Matematicki, 2021

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.

Some new primitive symmetric designs

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.

Primitive Symmetric Designs Having Up to 2500 Points

Matematička igra RasTpad

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.

Advances in Mathematics of Communications, 2016

This paper concerns the problem of the existence of Hadamard difference sets in nonabelian groups... more This paper concerns the problem of the existence of Hadamard difference sets in nonabelian groups of order 400. By introducing a new construction method, we construct new difference sets in 20 groups. We survey non-existence results, verifying non-existence in 45 groups.

Topology and its Applications, 2005

For each non-quadratic p-adic integer, p > 2, we give an example of a torus-like continuum Y (i.e... more For each non-quadratic p-adic integer, p > 2, we give an example of a torus-like continuum Y (i.e., inverse limit of an inverse sequence, where each term is the 2-torus T 2 and each bonding map is a surjective homomorphism), which admits three 4-sheeted covering maps f 0 : X 0 → Y, f 1 : X 1 → Y, f 2 : X 2 → Y such that the total spaces X 0 = Y, X 1 and X 2 are pair-wise non-homeomorphic. Furthermore, Y admits a 2p-sheeted covering map f 3 : X 3 → Y such that X 3 and Y are nonhomeomorphic. In particular, Y is not a self-covering space. This example shows that the class of self-covering spaces is not closed under the operation of forming inverse limits with open surjective bonding maps.

Journal of Combinatorial Designs, 2009

In this paper we either prove the non‐existence or give explicit construction of primitive symmet... more In this paper we either prove the non‐existence or give explicit construction of primitive symmetric (v, k, λ) designs with v=pm<2500, p prime and m>1. The method of design construction is based on an automorphism group action; non‐existence results additionally include the theory of difference sets, multiplier theorems in particular. The research involves programming and wide‐range computations. We make use of software package GAP and the library of primitive groups which it contains. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 141–154, 2010

Journal of Combinatorial Designs, 2011

By this article we conclude the construction of all primitive (v,k,k) symmetric designs with v<25... more By this article we conclude the construction of all primitive (v,k,k) symmetric designs with v<2500, up to a few unsolved cases. Complementary to the designs with prime power number of points published previously, here we give 55 primitive symmetric designs with v = p m , p prime and m positive integer, together with the analysis of their full automorphism groups. The research involves programming and wide-range computations. We make use of the software package GAP and the library of primitive groups which it contains.

Journal of Algebraic Combinatorics, 2013

We investigate the existence of difference sets in particular 2-groups. Being aware of the famous... more We investigate the existence of difference sets in particular 2-groups. Being aware of the famous necessary conditions derived from Turyn's and Ma's theorems, we develop a new method to cover necessary conditions for the existence of (2 2d+2 , 2 2d+1 -2 d , 2 2d -2 d ) difference sets, for some large classes of 2-groups. If a 2-group G possesses a normal cyclic subgroup x of order greater than 2 d+3+p , where the outer elements act on the cyclic subgroup similarly as in the dihedral, semidihedral, quaternion or modular groups and 2 p describes the size of G ∩ x or C G (x) ∩ x , then there is no difference set in such a group. Technically, we use a simple fact on how sums of 2 n -roots of unity can be annulated and use it to characterize properties of norm invariance (prescribed norm). This approach gives necessary conditions when a linear combination of 2 n -roots of unity remains unchanged under homomorphism actions in the sense of the norm.

Discrete Mathematics, 2007

The correspondence between a (96, 20, 4) symmetric design having regular automorphism group and a... more The correspondence between a (96, 20, 4) symmetric design having regular automorphism group and a difference set with the same parameters has been used to obtain difference sets in groups of order 96. Starting from eight such symmetric designs constructed by the tactical decomposition method, 55 inequivalent (96, 20, difference sets are distinguished. Thereby the existence of difference sets in 22 so far undecided nonabelian groups of order 96 is proved. 1991 Mathematics Subject ClassiÞcation. 05B05.

Designs, Codes and Cryptography, 2005

-symmetric design has been constructed, unique under the assumption of an automorphism group of o... more -symmetric design has been constructed, unique under the assumption of an automorphism group of order 576 action. The correspondence between a (96, 20, 4)-symmetric design having regular automorphism group and a difference set with the same parameters has been used to obtain difference sets in five nonabelian groups of order 96. None of them belongs to the class of groups that allow the application of so far known construction (McFarland, Dillon) for McFarland difference sets.