8th Croatian Mathematical Congress

Session

Combinatorics and Discrete Mathematics

CDM

2 Jul 2024, 16:05

D3 (School of Applied Mathematics and Informatics, J. J. Strossmayer University of Osijek)

Conveners

Combinatorics and Discrete Mathematics

• Snježana Majstorović Ergotić

Combinatorics and Discrete Mathematics

• Mario Pavčević

Combinatorics and Discrete Mathematics

• Marija Maksimović (Faculty of mathematics, University of Rijeka)

138. Directed regular graphs from groups

Matea Zubović Žutolija (Faculty of Mathematics, University of Rijeka)

02/07/2024, 16:05

CDM: Combinatorics and Discrete Mathematics

Talk

Regular directed graph $\mathrm{\Gamma }$ of degree $k$ with $n$ vertices is directed strongly regular graph, $DSRG(n,k,\lambda ,\mu ,t)$, if number of directed paths of length two from every vertex $v$ to every vertex $w$ is $\lambda$ if there exists directed edge $v\to w$, $t$ if $v=w$ and $\mu$ if there is no edge $v\to w$. Directed strongly regular graphs were introduced by Art Duval in 1988.
One...

104. $Kf-$ Šoltés problem

Dr Snježana Majstorović Ergotić (School of Applied Mathematics and Informatics)

02/07/2024, 16:25

CDM: Combinatorics and Discrete Mathematics

Talk

We study the $Kf-$ Šoltés problem, which is related to the resistance distance in a graph. While the original Šoltés problem deals with the identification of all graphs for which the removal of an arbitrary vertex preserves the Wiener index, the $Kf-$ Šoltés problem deals with graphs for which the removal of any vertex preserves the Kirchhoff index.
Currently, the only known solution to...

170. Counting divisions of the honeycomb strip

Luka Podrug

02/07/2024, 16:45

CDM: Combinatorics and Discrete Mathematics

Talk

Fibonacci numbers are one of the most famous and investigated sequences. They can be found almost everywhere. For example, the number of ways to tile a $1\times n$ rectangular strip using squares and dominoes is counted by Fibonacci numbers, as is the number of subsets of the set $\{1,2,\dots ,n\}$ without consecutive elements. Here we consider $2\times n$ hexagonal...

76. Genetic algorithms for construction of SRGs and DSRGs from orbit matrices

Dr Tin Zrinski (Fakultet za matematiku, Sveučilište u Rijeci)

03/07/2024, 16:05

CDM: Combinatorics and Discrete Mathematics

Talk

Genetic algorithms are search methods used in computing whose objective is to find exact or approximate solutions to optimization and search problems. A genetic algorithm mimics natural evolution, that is, it is based on optimizing a population (a subset of the entire search space). As in nature, the population consists of individuals that can reproduce and that can be affected by certain...

126. The existence of Steiner 2-designs $S(2,6,91)$ having ${\text{Frob}}_{26}$ as an automorphism group

Doris Dumičić Danilović (Faculty of Mathematics, University of Rijeka, Croatia)

03/07/2024, 16:25

CDM: Combinatorics and Discrete Mathematics

Talk

So far, there are only four known Steiner 2-designs $S(2,6,91)$ which have been found by C.J.Colbourn, M.J.Colbourn and W.H.Mills. Each of them is cyclic, i.e. having a cyclic automorphism group acting transitively on points. For more than 30 years no results about that designs have been published, and the last one is from 1991, when Z.Janko and V.D.Tonchev showed that any point-transitive ...

140. Cubes of symmetric designs

Mario Pavčević

03/07/2024, 16:45

CDM: Combinatorics and Discrete Mathematics

Talk

The concept of higher-dimensional combinatorial designs was introduced by Warwick de Launey in 1990. Recently we have studied higher-dimensional incidence structures. Since symmetric designs have the same number of points and blocks, their incidence matrices can easily be superposed to get a 3- or higher-dimensional binary cube. We have focused on 3-dimensional cubes of symmetric...

67. ON A CONSTRUCTION OF SELF-ORTHOGONAL CODES FROM ORBIT MATRICES OF 2-DESIGNS

Marija Maksimović (Faculty of Mathematics, University of Rijeka)

05/07/2024, 10:30

CDM: Combinatorics and Discrete Mathematics

Talk

The constructions of self-orthogonal codes from orbit matrices of $2$-designs has been extensively studied. In this talk we present new constructions of self-orthogonal codes from orbit matrices of $2$-designs for the cases not covered previously. We apply this construction on orbit matrices of $2$-$(1024,496,249)$ and $2$-$(45,5,1)$ designs and obtain some optimal self-orthogonal codes.

74. New extremal Type II ${\mathbb{Z}}_4$-codes via doubling method

Sara Ban (Faculty of Mathematics, University of Rijeka)

05/07/2024, 10:50

CDM: Combinatorics and Discrete Mathematics

Talk

The doubling method is a method for constructing Type II ${\mathbb{Z}}_4$-codes from a given Type II ${\mathbb{Z}}_4$-code.

Extremal Type II ${\mathbb{Z}}_4$-codes are a class of self-dual ${\mathbb{Z}}_4$-codes with Euclidean weights divisible by eight and the largest possible minimum Euclidean weight for a given length. A small number of such codes is known for lengths greater than or equal to...

78. LDPC LCD codes from odd graphs

Nina Mostarac (Faculty of Mathematics, University of Rijeka)

05/07/2024, 11:10

CDM: Combinatorics and Discrete Mathematics

Talk

In this talk we will describe binary LDPC LCD codes spanned by the adjacency matrices of the odd graphs as their parity-check matrices. For the odd graph $O_n$ ($n\ge 3$), the obtained code $C_n$ is an $(n,n)$-regular binary LDPC code of length $(\genfrac{}{}{0ex}{}{2n-1}{n-1})$, dimension $(\genfrac{}{}{0ex}{}{2n-2}{n-2})$, minimum distance $n+1$ and girth equal to $6$, which is also an LCD code (i.e. $C_n\cap...

133. Doubly even self-orthogonal codes from incidence and orbit matrices of quasi-symmetric designs

Ana Šumberac (Faculty of Mathematics, University of Rijeka)

05/07/2024, 11:30

CDM: Combinatorics and Discrete Mathematics

Talk

Construction and classification of self-orthogonal and self-dual codes is an active field of research. A code for which all codewords have weight divisible by four is called doubly even. Among self-orthogonal, especially self-dual codes, doubly even codes attract special attention. In this talk, we are dealing with some constructions of doubly even self-orthogonal linear codes from incidence...