Petkovšek, MarkoOverview
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Most widely held works by
Marko Petkovšek
A=B
by Marko Petkovšek
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Book
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13 editions published between 1995 and 2009 in English and Undetermined and held by 512 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
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Book
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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)
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Book
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3 editions published between 2007 and 2009 in Slovenian and held by 11 WorldCat member libraries worldwide
Računalniški slovarček : angleškoslovenski, slovenskoangleški
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Book
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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
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Book
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2 editions published between 1995 and 1997 in Slovenian and held by 9 WorldCat member libraries worldwide
The Zarankiewicz problem via Chow forms
by Marko Petkovšek
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Book
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4 editions published between 2000 and 2002 in English and held by 7 WorldCat member libraries worldwide We describe a connection between complexity of permanental ideals of generic matrices with the Zarankiewicz problem on the existence of complete bipartite subgraphs in bipartite graphs with sufficiently many edges
Gambler's ruin problem in several dimensions
by Andrej Kmet̕
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Book
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4 editions published between 2000 and 2002 in English and held by 7 WorldCat member libraries worldwide We give an explicit solution of the Gambler's Ruin Problem when the players use two or more currencies. We also determine the asymptotics of the expected duration of the game when both players have equal amounts of each currency
Ivan Vidav : 90 let : jubilejni zbornik
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Book
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1 edition published in 2008 in Slovenian and held by 7 WorldCat member libraries worldwide
Finding closedform solutions of difference equations by symbolic methods
by Marko Petkovšek
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Book
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5 editions published between 1990 and 1991 in English and held by 7 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
Letter graphs and wellquasiorder by induced subgraphs
by Marko Petkovšek
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Book
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4 editions published between 2000 and 2002 in English and held by 7 WorldCat member libraries worldwide Given a word $w$ over a finite alphabet and a set of ordered pairs of letters which define adjencies, we construct a graph which we call the letter graph of $w$. The lettericity of a graph $G$ is the least size of alphabet permitting to obtain $G$ as a letter graph. The set of 2letter graphs consists of treshold graphs, unboundedinterval graphs, and their complements. We determine the lettericity of cycles and bound the lettericity of paths to an interval of length one. We show that the class of $k$letter graphs is wellquasyordered by the induced subgraph relation, and that it has a finite set of minimal forbidden induced subgraphs. As a consequence, $k$letter graphs can be recognized in polynomial time for any fixed $k$
Discrete boundaryvalue problems
by Marko Petkovšek
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Book
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4 editions published between 2002 and 2003 in English and held by 6 WorldCat member libraries worldwide Obravnavane so linearne rekurzivne enačbe v več dimenzijah nad domeno, ki je dobljena iz prvega oktanta celoštevilske mreže z omejitvijo na začetni interval naravnih števil v nekaterih dimenzijah. Z metodo jedra je dobljen ekspliciten izraz za rodovno funkcijo rešitve v primeru, ko je omejena le ena dimenzija, apeks rekurzivne enačbe pa ima v vseh preostalih dimenzijah ničelne koordinate. Za razliko od začetnega problema (kjer je domena neomejena v vseh dimenzijah) z apeksom enakega tipa je tu rodovna funkcija rešitve racionalno odvisna od rodovnih funkcij robnih pogojev in desne strani enačbe. Kot primer uporabe so preštete mrežne poti med vzporednima hiperravninama z racionalnim naklonom. Z dvakratno uporabo metode jedra pa je rešen tudi primer diskretnega Dirichletovega problema v dveh dimenzijah
Uvod v računalništvo : naloge
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Book
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1 edition published in 1983 in Slovenian and held by 6 WorldCat member libraries worldwide
Nova zlata doba matematike
by Keith J Devlin
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Book
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1 edition published in 1993 in Slovenian and held by 5 WorldCat member libraries worldwide
Matematika : študijski programi 1. stopnje
by Fakulteta za matematiko in fiziko (Ljubljana)
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Book
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1 edition published in 2013 in Slovenian and held by 5 WorldCat member libraries worldwide
The Lah identity and the Argonauts
by Marko Petkovšek
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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)
D'Alembertian solutions of linear differential and difference equations
by Sergei A Abramov
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4 editions published in 1994 in English and French and held by 5 WorldCat member libraries worldwide D'Alembertove rešitve diferencialnih (diferenčnih) enačb so tiste, ki jih je mogoče izraziti kot vgnezdene nedoločene integrale (vsote) hipereksponentnih funkcij. Konstruiramo jih tako, da rekurzivno iščemo hipereksponentne rešitve in znižujemo red. Če poznamo d'Alembertovo rešitev enačbe $Ly=0$, lahko zapišemo ustrezne rešitve enačb $Ly=f$ in $L^\ast y=0$
On polynomial solutions of linear operator equations
by Sergei A Abramov
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4 editions published in 1995 in English and held by 5 WorldCat member libraries worldwide Polynomial solutions of linear difference, differential and $q$difference equations are usually constructed by first computing an upper bound $d$ on the degree of solutions and then using the method of undetermined coefficients. This leads to a system of linear equations with $d+1$ unknowns. The method described in the paper leads to a system with $r$ unknowns, where $r$ is the order of the equation
Combinatorial interpretation of unsigned Stirling and Lah numbers
by Marko Petkovšek
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Book
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3 editions published between 2002 and 2007 in English and held by 5 WorldCat member libraries worldwide The combinatorial role of unsigned Stirling and Lah numbers is reexamined in connection with ordinary powers, rising factorial powers, and falling factorial powers. Several bijective proofs are given
Izbrana poglavja iz računalništva
by Marko Petkovšek
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Book
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1 edition published in 1982 in Slovenian and held by 5 WorldCat member libraries worldwide
Special formal series solutions of linear operator equations
by Sergei A Abramov
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4 editions published between 1998 and 2000 in English and held by 5 WorldCat member libraries worldwide Transformacija, ki linearnemu operatorju priredi rekurzivno enačbo za koeficiente polinomskih vrst v njegovem jedru, je izomorfizem ustreznih operatorskih algeber. To izkoristimo pri razcepu $q$diferenčnih in rekurzivnih operatorjev ter pri iskanju rešitev linearnih diferencialnih enačb v obliki "lepih" potenčnih vrst. Med drugim karakteriziramo posplošene hipergeometrijske vrste, ki rešijo diferencialno enačbo v navadni točki, in pokažemo, da te rešitve ostanejo hipergeometrijske v vseh navadnih točkah enačbe. Da najdemo vse vse hipergeometrijske rešitve, je torej dovolj pregledati končno množico točk: vse singularne točke in poljubno navadno točko. Nadalje pokažemo, da v točki $x=a$ obstaja rešitev v obliki potenčne vrste s polinomskimi (racionalnimi) koeficienti le, če je enačba singularna v točki $x=a+1$ $(x=a)$ more
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Petkovsek, Marko.
ペトコブセク, マーコ
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