# Zoltan KasaSapientia Hungarian University of Transylvania, Cluj-Napoca · Department of Mathematics and informatics Târgu Mureș

Zoltan Kasa

PhD

## About

65

Publications

21,809

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136

Citations

Citations since 2016

Introduction

Zoltan Kasa currently is a retired professor at the Department of Mathematics and informatics Târgu Mureș, Sapientia Hungarian University of Transylvania, Cluj-Napoca. Zoltan does research in Algorithms, Computing in Mathematics, Natural Science, Engineering and Medicine and Data Structures. Their current project is 'graphs and interleaved networks'.

Additional affiliations

February 2008 - present

Education

October 1966 - June 1971

## Publications

Publications (65)

Special scattered subwords, in which the gaps are of length from a given set,
are defined. The scattered subword complexity, which is the number of such
scattered subwords, is computed for rainbow words.

In this paper we introduce and study a new complexity measure for finite
words. For positive integer $d$ special scattered subwords, called
super-$d$-subwords, in which the gaps are of length at least $(d-1)$, are
defined. We give methods to compute super-$d$-complexity (the total number of
different super-$d$-subwords) in the case of rainbow words...

We give two equivalent formulations of a conjecture [2,4] on the number of arc-disjoint Hamiltonian cycles in De Bruijn graphs.

Special scattered subwords in which the length of the gaps
are bounded by two natural numbers are considered. For rainbow words
the number of such scattered subwords is equal to the number of special
restricted compositions of natural numbers in which the components are
natural numbers from a given interval. Linear algorithms to compute
such number...

In randomly created structures (be they natural or artificial) very often there exist ordered substructures. In this Hungarian language scientific essay we present some of such structures in graph theory.

EN: We present the lengthy, almost three-year process of founding a university in Kolozsvár (Cluj) based on the contemporary press.
HU: A kolozsvári egyetemalapítás hosszadalmas, majdnem hároméves folyamatát mutatjuk be a korabeli sajtó alapján.

In this paper we deal with the life and scientific activity of fifteen renowned mathematician born in Kolozsvár/Cluj between 1800 and 1950.
KIVONAT
A dolgozat tizenöt, Kolozsváron 1800 és 1950 között született matematikus életét és munkásságát mutatja be.
Kulcsszavak: matematika, matematikusok, Kolozsvár

This survey presents the well-known Warshall's algorithm, a generalization and some interesting applications: transitive closure of relations, distances between vertices in graphs, number of paths in acyclic digraphs, all paths in digraphs, scattered complexity for rainbow words, special walks in finite automata.
\keywords Warshall's algorithm, Fl...

In this paper in Hungarian we deal with the life and activity of the mathematician and university professor Eugen Gergely (1896-1974).

The life and scientific and teaching activity of the professor in Mathematics Vilmos CSEKE (1915-1983) is presented.
CSEKE Vilmos matematikus a kolozsvári I. Ferdinánd Király Tudományegyetem matematikai szakát végezte, majd tizenkét évig matematikatanár volt a kolozsvári római katolikus (piarista) gimnáziumban, miközben az 1940-es években a Feren...

This booklet presents in Hungarian and English the life and activity of the American mathematician Abraham Wald born in Kolozsvár in 1902. The booklet mainly presents facts that are not very well known about his life and family.

In this paper we study the diffusion of a surfactant from a drop immersed in a liquid phase, giving the concentration profile and the thickness of the diffusion boundary layer.

This paper deals with the complexity of words (number of its distinct subwords), which play an important role in biology (nucleotide sequences), information theory and computer science. The new results are in Propositions 1-2 and in Lemma. A conjecture on the complexity of superstrings is stated. An old conjecture on frequency of words with some co...

The survey presents the well-known Warshall's algorithm, a generalization and some interesting applications of this.

Is this paper we accentuate the role of using graphs instead of transition functions in the definition of different type of automata (such finite, pushdown and Turing automata) for didactic purpose. Following this conception, the transition function, usefulness of which cannot be ignored, is introduced later not in the definition.

János Bolyai (1802-1860) is the greatest Hungarian mathematician who after recognizing the impossibility to prove Euclid's fifth (the so called parallel) postulate from Euclid's others, developed the absolute geometry (maybe the first non-Euclidian geometry) that is independent of the fifth postulate. He was only 21 years old when in 1823 he report...

Professor Antal Iványi, an active and always helpful member of our editorial board, passed away on January 8, 2017 at the age of 75. This paper deals with his life and activity.

This volume contains papers in Hungarian presented at the Gyula Vályi memorial conference held in Kolozsvár, 11-12 november 2004.

Let n, k and p be positive integers (2 ≤ n and 1 ≤ k ≤ n).
We rank the k largest numbers of n different numbers using at most p
processors. We organize a tournament consisting of pairwise matches
ending always with the win of the better player.
Let R(n, k, p) denote the minimal number of rounds, necessary to
rank the largest k given numbers (in wo...

Let d, m, and q be positive integers and A(q)={0,⋯,q-1} be an alphabet. We investigate a generalization of the well-known subword complexity of d-dimensional matrices containing the elements of A(q). Let ℒ=(L 1 ,⋯,L m ) be a list of distinct d-dimensional vectors, where L i =(a i1 ,⋯,a id ). The prism complexity of a d-dimensional q-ary matrix ℳ is...

In the paper are computed: the number of binary trees with n nodes and k
leaves; the number of leaves in the set of all binary trees with n nodes. These
are used to compute the number of states in the buddy system.

Algorithmic thinking is a valuable skill that all people should master. In this paper we propose a one-semester, algorithm-oriented computer science course for human science students. According to our experience such an initiative could succeed only if the next recipe is followed: interesting and practical content+ exciting didactical methods+ mini...

A coding method using binary sequences is presented for different computation problems related to Catalan numbers. This method proves in a very easy way the equivalence of these problems.

The subword complexity of a finite word $w$ of length $N$ is a function
which associates to each $n\le N$ the number of all distinct subwords of
$w$ having the length $n$. We define the \emph{maximal complexity} C(w)
as the maximum of the subword complexity for $n \in \{1,2,..., N \}$,
and the \emph{global maximal complexity} K(N) as the maximum of...

We present a method which displays all palindromes of a given length from De
Bruijn words of a certain order, and also a recursive one which constructs all
palindromes of length $n+1$ from the set of palindromes of length $n$. We show
that the palindrome complexity function, which counts the number of palindromes
of each length contained in a given...

This paper deals with the complexity of strings, which play an important role in biology (nucleotid sequences), information theory and computer science. The d-complexity of a string is defined as the number of its distinct d-substrings given in Definition 1. The case d=1 is studied in detail.

A new algorithm to generate all Dyck words is presented, which is used in ranking and unranking Dyck words. We emphasize the importance of using Dyck words in encoding objects related to Catalan numbers. As a consequence of formulas used in the ranking algorithm we can obtain a recursive formula for the nth Catalan number.

The palindrome complexity function palw of a word w attaches to each n∈N the number of palindromes (factors equal to their mirror images) of length n contained in w. The number of all the nonempty palindromes in a finite word is called the total palindrome complexity of that word. We present exact bounds for the total palindrome complexity and cons...

In the papers: [Tambulea, L., Data organization according to the property of consecutive retrieval, Mathematica, Revue d'analyse numerique et de theorie de l'approximation, 9, 2 (1980) 269--281.] and [Tambulea, L., Binary trees, an Euler's problem and finite sequences of numbers, Studia Univ. Babes-Bolyai, Mathematica, {35}, 3 (1990) 84--94.] L. Ta...

In the thesis we present novel techniques for semi-supervised classification by means of kernel methods. The three main parts of the thesis describe the proposed kernels: Wikipedia-based kernels for text categorization, hierarchical cluster kernels and reweighting kernels.

This chapter deals with the finite automata and regular languages, pushdown automata and context-free languages. The definition of automata is based on graph theory.

This book contains papers of the international conference held at Babes-Bolyai University (2005) in memoriam Gyula Farkas (1847–1930), professor in Physiscs and Mathematics at the Franz Joseph University in Kolozsvár between 1887 and 1915.

We deal with different types of dominating sets in de Bruijn graphs and prove a conjecture on perfect dominating sets.

Papers in memory of János Bolyai in Hungarian, Romanian, and English on the occasion of 200 years since his birth.

We define several notions of language complexity for finite words, and use them to define and compute some new complexity functions for infinite sequences. In particular, they give a new characterization of Sturmian sequences and discriminate between Sturmian sequences with bounded or unbounded partial quotients.

In this paper we deal with a graph model of the distributed database systems, in which the nearest sites with some given properties can be easily found.

The interface flow of an undeformable circular liquid lens in a liquid film, caused by interface active agents, is investigated by using the fundamental solution method and boundary element method.

The surface flow and the translational motion of a drop caused by interfacial tension gradients are investigated in the case of an undeformable drop, initially at rest (or at zero gravity). The interfacial tension gradients are induced by injecting the drop with surfactant. The spreading of the surfactant on the interface is described by a particul...

The paper deals with the possibility of detecting sequences of instructions in serial programs that can be executed in parallel.

## Projects

Projects (3)

Modelling by graphs networks that are interleaved having the same set of nodes.