Petkovšek, Marko
Overview
Works:  317 works in 407 publications in 2 languages and 1,030 library holdings 

Genres:  Dictionaries 
Roles:  Author, Thesis advisor, Editor, Translator, Other, Contributor 
Classifications:  QA76.15, 511.3028551 
Publication Timeline
.
Most widely held works by
Marko Petkovšek
A=B by
Marko Petkovšek(
Book
)
14 editions published between 1995 and 2009 in English and Undetermined and held by 510 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
14 editions published between 1995 and 2009 in English and Undetermined and held by 510 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
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
On Ore rings, linear operators and factorisation by
Manuel Bronstein(
Book
)
5 editions published in 1993 in English and held by 9 WorldCat member libraries worldwide
We first present the arithmetic of Ore polynomials, then describe how they can be wiewed as different types of linear operators, and finally give factorization algorithms for linear differential and difference operators, emphasizing the similarities between the two
5 editions published in 1993 in English and held by 9 WorldCat member libraries worldwide
We first present the arithmetic of Ore polynomials, then describe how they can be wiewed as different types of linear operators, and finally give factorization algorithms for linear differential and difference operators, emphasizing the similarities between the two
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
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
Uvod v računalništvo : naloge(
Book
)
1 edition published in 1983 in Slovenian and held by 6 WorldCat member libraries worldwide
1 edition published in 1983 in Slovenian and held by 6 WorldCat member libraries worldwide
Izbrana poglavja iz računalništva by
Marko Petkovšek(
Book
)
1 edition published in 1982 in Slovenian and held by 5 WorldCat member libraries worldwide
1 edition published in 1982 in Slovenian and held by 5 WorldCat member libraries worldwide
Gambler's ruin problem in several dimensions by
Andrej Kmet̕(
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
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
Special formal series solutions of linear operator equations by
Sergeĭ Abramov(
Book
)
4 editions published in 1998 in English and held by 5 WorldCat member libraries worldwide
The transformation which assigns to a linear operator $L$ the recurrence satisfied by coefficient sequences of the polynomual series in its kernel, is shown to be an isomorphism of the corresponding operator algebras. We use this fact to help factoring $q$difference and recurrence operators, and to find "nice" power series solutions of linear differential equations. In particular, we characterize generalized hypergeometric series that solve a linear differential equation with polynomial coefficients at an ordinary point of equation, and show that these solutions remain hypergeometric at any other ordinary point. Therefore to find all generalized hypergeometric series solutions, it suffices to look at a finite number of points: all the singular points, and a single, arbitrarily chosen ordinary point. We also show that at a point $x=a$ we can have power series solutions with: (1) polynomial coefficient sequence  only if the equation is singular at $a+1$, (2) nonpolynomial rational coefficient sequence  only if the equation is singular at $a$
4 editions published in 1998 in English and held by 5 WorldCat member libraries worldwide
The transformation which assigns to a linear operator $L$ the recurrence satisfied by coefficient sequences of the polynomual series in its kernel, is shown to be an isomorphism of the corresponding operator algebras. We use this fact to help factoring $q$difference and recurrence operators, and to find "nice" power series solutions of linear differential equations. In particular, we characterize generalized hypergeometric series that solve a linear differential equation with polynomial coefficients at an ordinary point of equation, and show that these solutions remain hypergeometric at any other ordinary point. Therefore to find all generalized hypergeometric series solutions, it suffices to look at a finite number of points: all the singular points, and a single, arbitrarily chosen ordinary point. We also show that at a point $x=a$ we can have power series solutions with: (1) polynomial coefficient sequence  only if the equation is singular at $a+1$, (2) nonpolynomial rational coefficient sequence  only if the equation is singular at $a$
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 irrational chess knight by
Marko Petkovšek(
Book
)
4 editions published in 1998 in English and held by 5 WorldCat member libraries worldwide
Podani so zadostni pogoji za racionalnost oziroma algebraičnost rodovnih funkcij rešitev linearnih parcialnih rekurzivnih enačb s konstantnimi koeficienti. Predstavljen je primer, kjer je rodovna funkcija iracionalna in morda celo transcedentna
4 editions published in 1998 in English and held by 5 WorldCat member libraries worldwide
Podani so zadostni pogoji za racionalnost oziroma algebraičnost rodovnih funkcij rešitev linearnih parcialnih rekurzivnih enačb s konstantnimi koeficienti. Predstavljen je primer, kjer je rodovna funkcija iracionalna in morda celo transcedentna
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
Multibasic and mixed Gosper's algorithm by
A Bauer(
Book
)
4 editions published in 1998 in English and held by 5 WorldCat member libraries worldwide
Gosperjev sumacijski algoritem poišče hipergeometrijsko zaključeno obliko nedoločene vsote s hipergeometrijskimi členi, če takšna oblika obstaja. Gosperjev algoritem posplošimo na primer, ko so členi hkrati hipergeometrijski in multibazni $q$hipergeometrijski. Podani so tudi algoritmi za računanje hipergeometrijske kanonske oblike racionalnih funkcij in za iskanje polinomskih rešitev rekurzivnih enačb v multibaznem in mešanem primeru
4 editions published in 1998 in English and held by 5 WorldCat member libraries worldwide
Gosperjev sumacijski algoritem poišče hipergeometrijsko zaključeno obliko nedoločene vsote s hipergeometrijskimi členi, če takšna oblika obstaja. Gosperjev algoritem posplošimo na primer, ko so členi hkrati hipergeometrijski in multibazni $q$hipergeometrijski. Podani so tudi algoritmi za računanje hipergeometrijske kanonske oblike racionalnih funkcij in za iskanje polinomskih rešitev rekurzivnih enačb v multibaznem in mešanem primeru
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
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)
Matematika : študijski programi 1. stopnje by Fakulteta za matematiko in fiziko (Ljubljana)(
Book
)
1 edition published in 2013 in Slovenian and held by 5 WorldCat member libraries worldwide
1 edition published in 2013 in Slovenian and held by 5 WorldCat member libraries worldwide
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Related Identities
 Wilf, Herbert S. 19312012
 Zeilberger, Doron
 Knuth, Donald Ervin 1938 Author of introduction
 Pisanski, Tomaž Author
 Mohar, Bojan Author
 Abramov, Sergei A. 1944 Author Translator
 Bauer, Andrej Author Editor
 Željko, Matjaž Other Author Editor
 Rapoša, Kazimir Editor
 Gams, Matjaž Author Editor
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