Petkovšek, Marko
Overview
Works:  250 works in 331 publications in 3 languages and 939 library holdings 

Genres:  Dictionaries 
Roles:  Author, Thesis advisor, Editor, Translator, Contributor, Other 
Classifications:  QA164.9, 511.3028551 
Publication Timeline
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Most widely held works by
Marko Petkovšek
A=B by
Marko Petkovšek(
Book
)
20 editions published between 1995 and 2009 in 3 languages and held by 520 WorldCat member libraries worldwide
In the area of combinatorial identities computers are able to find very elegant proofs of difficult theorems unassisted by human intervention. This autonomy means that not only is it possible to use a PC to find such a proof, but also the proof can be checked easily. This book shows how several recently developed computer algorithms can master the difficult job of simplifying complex summations and if there is no such simplification they will prove this to be the case. The authors present the underlying mathematical theory of these methods, the principle theorems and proofs, and include a package of computer programs that can do these tasks
20 editions published between 1995 and 2009 in 3 languages and held by 520 WorldCat member libraries worldwide
In the area of combinatorial identities computers are able to find very elegant proofs of difficult theorems unassisted by human intervention. This autonomy means that not only is it possible to use a PC to find such a proof, but also the proof can be checked easily. This book shows how several recently developed computer algorithms can master the difficult job of simplifying complex summations and if there is no such simplification they will prove this to be the case. The authors present the underlying mathematical theory of these methods, the principle theorems and proofs, and include a package of computer programs that can do these tasks
Računalništvo(
Book
)
2 editions published between 1988 and 1991 in Slovenian and held by 18 WorldCat member libraries worldwide
Lexicon describes various terms connected to the computer science, including history of computer science, hardware, software, computing, theoretical computer science. Some mathematical fields used in computer science are also well covered: logic, set theory, graph theory, combinatorics, algebra, numerical mathematics, probability and statistics
2 editions published between 1988 and 1991 in Slovenian and held by 18 WorldCat member libraries worldwide
Lexicon describes various terms connected to the computer science, including history of computer science, hardware, software, computing, theoretical computer science. Some mathematical fields used in computer science are also well covered: logic, set theory, graph theory, combinatorics, algebra, numerical mathematics, probability and statistics
Predstavitev študijskih programov iz matematike by Fakulteta za matematiko in fiziko (Ljubljana)(
Book
)
3 editions published between 2007 and 2009 in Slovenian and held by 11 WorldCat member libraries worldwide
3 editions published between 2007 and 2009 in Slovenian and held by 11 WorldCat member libraries worldwide
Izbrana poglavja iz računalništva by
Marko Petkovšek(
Book
)
3 editions published between 1982 and 1986 in Slovenian and held by 10 WorldCat member libraries worldwide
3 editions published between 1982 and 1986 in Slovenian and held by 10 WorldCat member libraries worldwide
Računalniški slovarček : angleškoslovenski, slovenskoangleški(
Book
)
1 edition published in 1993 in English and held by 9 WorldCat member libraries worldwide
Angleškoslovenski in slovenskoangleški slovar računalniškega izrazoslovja
1 edition published in 1993 in English and held by 9 WorldCat member libraries worldwide
Angleškoslovenski in slovenskoangleški slovar računalniškega izrazoslovja
Altius, citius, fortius : [izbrana poglavja iz matematike za srednješolce] by
Matjaž Željko(
Book
)
2 editions published between 1995 and 1997 in Slovenian and held by 9 WorldCat member libraries worldwide
2 editions published between 1995 and 1997 in Slovenian and held by 9 WorldCat member libraries worldwide
Finding closedform solutions of difference equations by symbolic methods by
Marko Petkovšek(
Book
)
6 editions published between 1990 and 1991 in English and held by 8 WorldCat member libraries worldwide
This thesis investigates symbolic computation in the domain of difference equations. The goal is to obtain explicit solutions of a given equation automatically and, when possible, in closed form
6 editions published between 1990 and 1991 in English and held by 8 WorldCat member libraries worldwide
This thesis investigates symbolic computation in the domain of difference equations. The goal is to obtain explicit solutions of a given equation automatically and, when possible, in closed form
Ivan Vidav : 90 let : jubilejni zbornik(
Book
)
1 edition published in 2008 in Slovenian and held by 7 WorldCat member libraries worldwide
1 edition published in 2008 in Slovenian and held by 7 WorldCat member libraries worldwide
Tekmujmo za Vegova priznanja : zbirka rešenih nalog iz matematike za učence petih in šestih razredov osnovnih šol by Pavel Zajc(
Book
)
2 editions published in 1987 in Slovenian and held by 6 WorldCat member libraries worldwide
2 editions published in 1987 in Slovenian and held by 6 WorldCat member libraries worldwide
Nova zlata doba matematike by Keith Devlin(
Book
)
1 edition published in 1993 in Slovenian and held by 5 WorldCat member libraries worldwide
1 edition published in 1993 in Slovenian and held by 5 WorldCat member libraries worldwide
The Zarankiewicz problem via Chow forms by
Marko Petkovšek(
Book
)
3 editions published in 2000 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 2000 in English and held by 5 WorldCat member libraries worldwide
The Lah identity and the Argonauts by
Marko Petkovšek(
Book
)
3 editions published in 2002 in English and held by 5 WorldCat member libraries worldwide
Podan je kombinatoričen dokaz Lahove identitete (razvoja naraščajoče potence po padajočih potencah)
3 editions published in 2002 in English and held by 5 WorldCat member libraries worldwide
Podan je kombinatoričen dokaz Lahove identitete (razvoja naraščajoče potence po padajočih potencah)
Letter graphs and wellquasiorder by induced subgraphs by
Marko Petkovšek(
Book
)
3 editions published in 2000 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 2000 in English and held by 5 WorldCat member libraries worldwide
Combinatorial interpretation of unsigned Stirling and Lah numbers by
Marko Petkovšek(
Book
)
3 editions published in 2002 in English and held by 5 WorldCat member libraries worldwide
Na novo je osvetljena vloga nepredznačenih Stirlingovih in Lahovih števil v povezavi z navadnimi, naraščajočimi in padajočimi potencami. Podanih je več bijektivnih dokazov pripadajočih identitet
3 editions published in 2002 in English and held by 5 WorldCat member libraries worldwide
Na novo je osvetljena vloga nepredznačenih Stirlingovih in Lahovih števil v povezavi z navadnimi, naraščajočimi in padajočimi potencami. Podanih je več bijektivnih dokazov pripadajočih identitet
Discrete boundaryvalue problems by
Marko Petkovšek(
Book
)
3 editions published in 2003 in English and held by 5 WorldCat member libraries worldwide
We consider multivariate sequences, defined by a partial linear reccurence equation togrther with appropriate boundary conditions. The domain of definition of these sequences is first orthant of the integer lattice restricted in some dimensions to an initial segment of the nonnegative integers. By means of the kernel method we obtain an explicit expression for the generating function of the solution in the case of a single restricted dimension, provided by the apex of the recurrence vanishes in all the remaining dimensions. Unlike the initialvalue problem (where the domain is unrestricted in all dimensions) with apex of this type, this generating function depends rationally on the generating functions of the boundary conditions and of the righthand side of the recurrence equation. As an example, we count lattice paths between two parallel hyperplanes with rational incline. By using the kernel method twice we also solve a discrete Dirichlet problem in two dimensions
3 editions published in 2003 in English and held by 5 WorldCat member libraries worldwide
We consider multivariate sequences, defined by a partial linear reccurence equation togrther with appropriate boundary conditions. The domain of definition of these sequences is first orthant of the integer lattice restricted in some dimensions to an initial segment of the nonnegative integers. By means of the kernel method we obtain an explicit expression for the generating function of the solution in the case of a single restricted dimension, provided by the apex of the recurrence vanishes in all the remaining dimensions. Unlike the initialvalue problem (where the domain is unrestricted in all dimensions) with apex of this type, this generating function depends rationally on the generating functions of the boundary conditions and of the righthand side of the recurrence equation. As an example, we count lattice paths between two parallel hyperplanes with rational incline. By using the kernel method twice we also solve a discrete Dirichlet problem in two dimensions
The irrational chess knight by
Marko Petkovšek(
Book
)
4 editions published in 1998 in English and held by 5 WorldCat member libraries worldwide
Sufficient conditions for generating functions of solutions of linear partial recurrences with constant coefficients to be rational resp. algebraic are given. An example is presented where the generating function is irrational and is suspected to be transcendental
4 editions published in 1998 in English and held by 5 WorldCat member libraries worldwide
Sufficient conditions for generating functions of solutions of linear partial recurrences with constant coefficients to be rational resp. algebraic are given. An example is presented where the generating function is irrational and is suspected to be transcendental
On Ore rings, linear operators and factorisation by
Manuel Bronstein(
Book
)
3 editions published in 1993 in English and held by 5 WorldCat member libraries worldwide
Predstavljena je aritmetika Orejevih polinomov in delovanje Orejevih polinomov kot operatorjev različnih tipov. Podan je algoritem za faktorizacijo linearnih diferencialnih in diferenčnih operatorjev na nerazcepne faktorje
3 editions published in 1993 in English and held by 5 WorldCat member libraries worldwide
Predstavljena je aritmetika Orejevih polinomov in delovanje Orejevih polinomov kot operatorjev različnih tipov. Podan je algoritem za faktorizacijo linearnih diferencialnih in diferenčnih operatorjev na nerazcepne faktorje
Counting disconnected structures by
Marko Petkovšek(
Book
)
3 editions published in 2005 in English and held by 4 WorldCat member libraries worldwide
When counting isomers with a given number of atoms one usually assumes that we want to count (connected) molecules. In this note we present a method that can be used for counting disconnected structures if counts of connected structures are given. The method can be used also in the reverse direction. If the numbers of all structures are known, the number of connected structures can be readily determined
3 editions published in 2005 in English and held by 4 WorldCat member libraries worldwide
When counting isomers with a given number of atoms one usually assumes that we want to count (connected) molecules. In this note we present a method that can be used for counting disconnected structures if counts of connected structures are given. The method can be used also in the reverse direction. If the numbers of all structures are known, the number of connected structures can be readily determined
Finding all hypergeometric solutions of linear differential equations by
Marko Petkovšek(
Book
)
4 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
4 editions published in 1993 in English and held by 4 WorldCat member libraries worldwide
Simbolno reševanje linearnih funkcijskih enačb v obliki polinomskih vrst : disertacija by Helena Zakrajšek(
Book
)
1 edition published in 2003 in Slovenian and held by 4 WorldCat member libraries worldwide
In symbolic computation exact solutions of functional equations $Ly=f$, where $L$ is a linear operator, are of great interest. One of the oldest and wellknown methods of solving linear differential equations is Frobenious method of power swries to a differential equation $Ly=0$ assigns a recurrence equation ${\mathcal L}c = 0$ valid for the coefficient sequence. The method can be generalized in a way that we use: (1) other types of operators (fifference, $q$differential) and (2) different polynomial families. We reduce questions about operators of different types to questions about operators of a single type, namely recurrence operators. Here we deal with before mentioned operators and seek the hypergeometric series solutions. Let ${\mathcal B} = \{P_n*X)}$ be a polynomial basis and $L$ a linear operator, that transforms $P_n$ to a linear combination (of fixed length) of elements of basis ${\mathcal B}$. In the first chapter we define a transformation which to operator $L$ assigns a recurrence operator ${\mathcal R_B}L$, such that $L\sum c_nP_n = \sum{\mathcal R_B}L(c_n)$, which also turned out to be an isomorphism of algebras of operators. In the second chapter we define an automorphism ${\mathcal D}_\alpha$ of differential operators with polynomial coefficients and the Hermite integral transformation ${\mathcal H}_\alpha$ with the following property: if a solution $f$ of $({\mathcal D}_\alpha)y = 0$ is known ${\mathcal H}_\alpha(f)$ (when exists) is a solution of $Ly=0$. We introduced the algorithm that compute the Hermite transform of a rational function and use it to construct $n+1$ linearly independent solutions of $Ly=0$ when $({\mathcal D}_\alpha L)y = 0$ has a rational solution with $n$ distinct poles. In the next chapter we search for formal hypergeometric series solutions of differential (difference, $q$differential) equations. We show that using special hypergeometric polynomial families and rewriting the operator in a special form anable us to construct a recurrence relation of minimal order. In the last chapter we prove a slighyly generalized Bacher's conjecture that a sequence of principal minors of an infinite Pascallike matrix satisfies a linear recurrence with constant or exponential coefficients. In order to do that we first show that a sequence of principal minors of banddiagonal matrix satisfies a linear recurrence, than we describe how a Pascallike matrix is transformed to such a form
1 edition published in 2003 in Slovenian and held by 4 WorldCat member libraries worldwide
In symbolic computation exact solutions of functional equations $Ly=f$, where $L$ is a linear operator, are of great interest. One of the oldest and wellknown methods of solving linear differential equations is Frobenious method of power swries to a differential equation $Ly=0$ assigns a recurrence equation ${\mathcal L}c = 0$ valid for the coefficient sequence. The method can be generalized in a way that we use: (1) other types of operators (fifference, $q$differential) and (2) different polynomial families. We reduce questions about operators of different types to questions about operators of a single type, namely recurrence operators. Here we deal with before mentioned operators and seek the hypergeometric series solutions. Let ${\mathcal B} = \{P_n*X)}$ be a polynomial basis and $L$ a linear operator, that transforms $P_n$ to a linear combination (of fixed length) of elements of basis ${\mathcal B}$. In the first chapter we define a transformation which to operator $L$ assigns a recurrence operator ${\mathcal R_B}L$, such that $L\sum c_nP_n = \sum{\mathcal R_B}L(c_n)$, which also turned out to be an isomorphism of algebras of operators. In the second chapter we define an automorphism ${\mathcal D}_\alpha$ of differential operators with polynomial coefficients and the Hermite integral transformation ${\mathcal H}_\alpha$ with the following property: if a solution $f$ of $({\mathcal D}_\alpha)y = 0$ is known ${\mathcal H}_\alpha(f)$ (when exists) is a solution of $Ly=0$. We introduced the algorithm that compute the Hermite transform of a rational function and use it to construct $n+1$ linearly independent solutions of $Ly=0$ when $({\mathcal D}_\alpha L)y = 0$ has a rational solution with $n$ distinct poles. In the next chapter we search for formal hypergeometric series solutions of differential (difference, $q$differential) equations. We show that using special hypergeometric polynomial families and rewriting the operator in a special form anable us to construct a recurrence relation of minimal order. In the last chapter we prove a slighyly generalized Bacher's conjecture that a sequence of principal minors of an infinite Pascallike matrix satisfies a linear recurrence with constant or exponential coefficients. In order to do that we first show that a sequence of principal minors of banddiagonal matrix satisfies a linear recurrence, than we describe how a Pascallike matrix is transformed to such a form
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Related Identities
 Zeilberger, Doron
 Wilf, Herbert S. 19312012
 Knuth, Donald Ervin 1938 Author of introduction
 Mohar, Bojan Author
 Bauer, Andrej Author Editor
 Rapoša, Kazimir Editor
 Cimprič, Jaka Editor
 Pisanski, Tomaž
 Gams, Matjaž računalništvo Editor
 Dobrin, Andrej
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