# zbMATH — the first resource for mathematics

## Korec, Ivan

Compute Distance To:
 Author ID: korec.ivan Published as: Korec, Ivan; Korec, I.
 Documents Indexed: 69 Publications since 1966
all top 5

#### Co-Authors

 57 single-authored 2 Procházka, Juraj 2 Rautenberg, Wolfgang 2 Znam, Stefan 1 Benešová, Mária 1 Bès, Alexis 1 Borsík, Ján 1 Gregusova, Ludmila 1 Najar, Rudolph M. 1 Peretyat’kin, Mikhail G. 1 Wiedermann, Jiří
all top 5

#### Serials

 9 Mathematica Slovaca 8 Acta Mathematica Universitatis Comenianae 5 Acta Facultatis Rerum Naturalium Universitatis Comenianae. Mathematica 3 Fundamenta Mathematicae 3 Theoretical Computer Science 3 Computers and Artificial Intelligence 2 Časopis Pro Pěstování Matematiky 2 Proceedings of the American Mathematical Society 2 Tatra Mountains Mathematical Publications 1 American Mathematical Monthly 1 Archiv für Mathematische Logik und Grundlagenforschung 1 Discrete Mathematics 1 Acta Arithmetica 1 The Fibonacci Quarterly 1 Annales Societatis Mathematicae Polonae. Series IV 1 Annals of Pure and Applied Logic 1 Prace Naukowe Uniwersytetu Śląskiego w Katowicach. Annales Mathematicae Silesianae 1 Elektronische Informationsverarbeitung und Kybernetik 1 Wissenschaftliche Zeitschrift der Humboldt-Universität zu Berlin. Mathematisch-Naturwissenschaftliche Reihe 1 Grazer Mathematische Berichte 1 Acta Universitatis Matthiae Belii. Series Mathematics 1 Acta Mathematica et Informatica Universitatis Ostraviensis 1 Bulletin de l’Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques
all top 5

#### Fields

 31 Number theory (11-XX) 27 Mathematical logic and foundations (03-XX) 19 Computer science (68-XX) 10 General algebraic systems (08-XX) 7 Combinatorics (05-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Group theory and generalizations (20-XX) 2 Real functions (26-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Operator theory (47-XX) 1 General topology (54-XX) 1 Probability theory and stochastic processes (60-XX)

#### Citations contained in zbMATH Open

44 Publications have been cited 149 times in 101 Documents Cited by Year
Small universal register machines. Zbl 0874.68105
Korec, Ivan
1996
A list of arithmetical structures complete with respect to the first-order definability. Zbl 0971.03035
Korec, I.
2001
On a generalization of Mycielski’s and Znam’s conjectures about coset decomposition of Abelian groups. Zbl 0286.20053
Korec, Ivan
1974
Asymptotical densities in generalized Pascal triangles. Zbl 0612.68048
Korec, Ivan
1986
A ternary function for distributivity and permutability of an equivalence lattice. Zbl 0382.08004
Korec, Ivan
1978
On disjoint covering of groups by their cosets. Zbl 0389.20031
Korec, Ivan; Znám, Štefan
1977
Generalized Pascal triangles. Decidability results. Zbl 0607.05002
Korec, Ivan
1985
Irreducible disjoint covering systems. Zbl 0519.10002
Korec, Ivan
1984
Definability of arithmetic operations in Pascal triangle modulo an integer divisible by two primes. Zbl 0797.11024
Korec, Ivan
1993
Definability of addition from multiplication and neighbourhood relation and some related results. Zbl 0877.03026
Korec, Ivan
1996
Model-interpretability into trees and applications. Zbl 0324.02041
Korec, Ivan; Rautenberg, Wolfgang
1976
Deterministic verification of integer matrix multiplication in quadratic time. Zbl 1432.68620
Korec, Ivan; Wiedermann, Jiří
2014
Structures related to Pascal’s triangle modulo 2 and their elementary theories. Zbl 0824.11008
Korec, Ivan
1994
Nonexistence of a small perfect rational cuboid. II. Zbl 0555.10006
Korec, Ivan
1984
Palindromic squares for various number system bases. Zbl 0755.11004
Korec, Ivan
1991
Irrational speeds of configurations growth in generalized Pascal triangles. Zbl 0786.68072
Korec, Ivan
1993
Definability within structures related to Pascal’s triangle modulo an integer. Zbl 0905.11013
Bès, Alexis; Korec, Ivan
1998
Undecidability and uniform definability in classes of structures related to Pascal triangles modulo $$n$$. Zbl 0974.03007
Korec, Ivan
1997
Theories of generalized Pascal triangles. Zbl 0889.11009
Korec, Ivan
1997
Substantially different theories of two structures associated to the same generalized Pascal triangle. Zbl 0822.03008
Korec, Ivan
1994
Undecidable elementary theories of classes of generalized Pascal triangles. Zbl 0856.03008
Korec, Ivan
1995
A density estimate for the $$3x+1$$ problem. Zbl 0797.11027
Korec, Ivan
1994
Decidable and undecidable theories of generalized Pascal triangles. Zbl 0813.03006
Korec, I.
1995
Definability in structures of finite valency. Zbl 0276.02036
Korec, I.; Peretyat’kin, M. G.; Rautenberg, W.
1974
Concrete representation of some equivalence lattices. Zbl 0458.08002
Korec, Ivan
1981
Small universal Minsky machines. Zbl 0412.03019
Gregusova, Ludmila; Korec, Ivan
1979
Pascal triangles modulo n and modular trellises. Zbl 0695.68055
Korec, Ivan
1990
Elementary definability from Pascal’s triangle modulo $$p$$ and the set of $$e$$-th powers. Zbl 0944.03004
Korec, Ivan
1998
Additive conditions on sums of squares. Zbl 0924.11004
Korec, Ivan
1998
Definability of Pascal’s triangles modulo 4 and 6 and some other binary operations from their associated equivalence relations. Zbl 0882.11013
Korec, Ivan
1996
On number of cosets in non-natural disjoint covering systems. Zbl 0704.11005
Korec, I.
1990
Generalized Pascal triangles. Zbl 0734.68072
Korec, Ivan
1989
Real-time generation of primes by a one-dimensional cellular automaton with 11 states. Zbl 0941.68084
Korec, Ivan
1997
Definability of arithmetic operations from the order and a random relation. Zbl 0788.03070
Korec, Ivan
1993
A complexity valuation of the partial recursive functions following the expectation of the length of their computations on Minsky machines. Zbl 0215.32203
Korec, I.
1970
A class of Lebesgue non-measurable subfields of the field of real numbers. Zbl 0243.28003
Korec, Ivan
1972
A representation of $$\Sigma_1$$-functions as compositions of $$\Sigma_0$$- functions in Gödel-Bernays set theory with the axiom of constructibility. Zbl 0292.02053
Korec, I.
1974
On a problem of V. Ptak. Zbl 0429.26001
Korec, Ivan
1978
Semilinear real-time systolic trellis automata. Zbl 0756.68079
Korec, Ivan
1989
Irreducible disjoint covering systems of $${\mathbb{Z}}$$ with the common modulus consisting of three primes. Zbl 0612.10002
Korec, Ivan
1985
Improvement of Mycielski’s inequality for non-natural disjoint covering systems of $${\mathbb{Z}}$$. Zbl 0612.10003
Korec, Ivan
1987
Multiples of an integer in the Pascal triangle. Zbl 0615.10003
Korec, Ivan
1985
Nonexistence of a small perfect rational cuboid. Zbl 0541.10019
Korec, Ivan
1983
Lower bounds for perfect rational cuboids. Zbl 0771.11016
Korec, Ivan
1992
Deterministic verification of integer matrix multiplication in quadratic time. Zbl 1432.68620
Korec, Ivan; Wiedermann, Jiří
2014
A list of arithmetical structures complete with respect to the first-order definability. Zbl 0971.03035
Korec, I.
2001
Definability within structures related to Pascal’s triangle modulo an integer. Zbl 0905.11013
Bès, Alexis; Korec, Ivan
1998
Elementary definability from Pascal’s triangle modulo $$p$$ and the set of $$e$$-th powers. Zbl 0944.03004
Korec, Ivan
1998
Additive conditions on sums of squares. Zbl 0924.11004
Korec, Ivan
1998
Undecidability and uniform definability in classes of structures related to Pascal triangles modulo $$n$$. Zbl 0974.03007
Korec, Ivan
1997
Theories of generalized Pascal triangles. Zbl 0889.11009
Korec, Ivan
1997
Real-time generation of primes by a one-dimensional cellular automaton with 11 states. Zbl 0941.68084
Korec, Ivan
1997
Small universal register machines. Zbl 0874.68105
Korec, Ivan
1996
Definability of addition from multiplication and neighbourhood relation and some related results. Zbl 0877.03026
Korec, Ivan
1996
Definability of Pascal’s triangles modulo 4 and 6 and some other binary operations from their associated equivalence relations. Zbl 0882.11013
Korec, Ivan
1996
Undecidable elementary theories of classes of generalized Pascal triangles. Zbl 0856.03008
Korec, Ivan
1995
Decidable and undecidable theories of generalized Pascal triangles. Zbl 0813.03006
Korec, I.
1995
Structures related to Pascal’s triangle modulo 2 and their elementary theories. Zbl 0824.11008
Korec, Ivan
1994
Substantially different theories of two structures associated to the same generalized Pascal triangle. Zbl 0822.03008
Korec, Ivan
1994
A density estimate for the $$3x+1$$ problem. Zbl 0797.11027
Korec, Ivan
1994
Definability of arithmetic operations in Pascal triangle modulo an integer divisible by two primes. Zbl 0797.11024
Korec, Ivan
1993
Irrational speeds of configurations growth in generalized Pascal triangles. Zbl 0786.68072
Korec, Ivan
1993
Definability of arithmetic operations from the order and a random relation. Zbl 0788.03070
Korec, Ivan
1993
Lower bounds for perfect rational cuboids. Zbl 0771.11016
Korec, Ivan
1992
Palindromic squares for various number system bases. Zbl 0755.11004
Korec, Ivan
1991
Pascal triangles modulo n and modular trellises. Zbl 0695.68055
Korec, Ivan
1990
On number of cosets in non-natural disjoint covering systems. Zbl 0704.11005
Korec, I.
1990
Generalized Pascal triangles. Zbl 0734.68072
Korec, Ivan
1989
Semilinear real-time systolic trellis automata. Zbl 0756.68079
Korec, Ivan
1989
Improvement of Mycielski’s inequality for non-natural disjoint covering systems of $${\mathbb{Z}}$$. Zbl 0612.10003
Korec, Ivan
1987
Asymptotical densities in generalized Pascal triangles. Zbl 0612.68048
Korec, Ivan
1986
Generalized Pascal triangles. Decidability results. Zbl 0607.05002
Korec, Ivan
1985
Irreducible disjoint covering systems of $${\mathbb{Z}}$$ with the common modulus consisting of three primes. Zbl 0612.10002
Korec, Ivan
1985
Multiples of an integer in the Pascal triangle. Zbl 0615.10003
Korec, Ivan
1985
Irreducible disjoint covering systems. Zbl 0519.10002
Korec, Ivan
1984
Nonexistence of a small perfect rational cuboid. II. Zbl 0555.10006
Korec, Ivan
1984
Nonexistence of a small perfect rational cuboid. Zbl 0541.10019
Korec, Ivan
1983
Concrete representation of some equivalence lattices. Zbl 0458.08002
Korec, Ivan
1981
Small universal Minsky machines. Zbl 0412.03019
Gregusova, Ludmila; Korec, Ivan
1979
A ternary function for distributivity and permutability of an equivalence lattice. Zbl 0382.08004
Korec, Ivan
1978
On a problem of V. Ptak. Zbl 0429.26001
Korec, Ivan
1978
On disjoint covering of groups by their cosets. Zbl 0389.20031
Korec, Ivan; Znám, Štefan
1977
Model-interpretability into trees and applications. Zbl 0324.02041
Korec, Ivan; Rautenberg, Wolfgang
1976
On a generalization of Mycielski’s and Znam’s conjectures about coset decomposition of Abelian groups. Zbl 0286.20053
Korec, Ivan
1974
Definability in structures of finite valency. Zbl 0276.02036
Korec, I.; Peretyat&rsquo;kin, M. G.; Rautenberg, W.
1974
A representation of $$\Sigma_1$$-functions as compositions of $$\Sigma_0$$- functions in Gödel-Bernays set theory with the axiom of constructibility. Zbl 0292.02053
Korec, I.
1974
A class of Lebesgue non-measurable subfields of the field of real numbers. Zbl 0243.28003
Korec, Ivan
1972
A complexity valuation of the partial recursive functions following the expectation of the length of their computations on Minsky machines. Zbl 0215.32203
Korec, I.
1970
all top 5

#### Cited by 137 Authors

 14 Korec, Ivan 6 Pan, Linqiang 6 Păun, Gheorghe 6 Verlan, Sergey 5 Pérez-Jiménez, Mario J. 4 Păun, Andrei 4 Peng, Hong 4 Wang, Jun 3 Alhazov, Artiom 3 Berger, Marc A. 3 Felzenbaum, Alexander 3 Fraenkel, Aviezri Siegmund 3 Freund, Rudolf 3 Jiang, Suxia 3 Porubsky, Stefan 3 Shallit, Jeffrey O. 3 Zeng, Xiangxiang 2 Bao, Tingting 2 Barbé, André M. 2 Bîlbîe, Florin-Daniel 2 Cegielski, Patrick 2 Fan, Jihui 2 Lingas, Andrzej 2 Margenstern, Maurice 2 Mauri, Giancarlo 2 Neary, Turlough 2 Richard, Denis 2 Speranski, Stanislav O. 2 von Haeseler, Fritz 2 Wang, Yanfeng 2 Wirsching, Günther J. 2 Wu, Tingfang 2 Yang, Qian 1 Alkauskas, Giedrius 1 Allouche, Jean-Paul Simon 1 Andrews, Uri 1 Beebee, John 1 Bès, Alexis 1 Bridy, Andrew 1 Brunotte, Horst 1 Cazzaniga, Paolo 1 Chajda, Ivan 1 Chen, Haiming 1 Chen, Xu 1 Chen, Yonggao 1 Chouraqui, Fabienne 1 Compton, Kevin J. 1 Csuhaj-Varjú, Erzsébet 1 Dumitrache, Ion 1 Durand-Lose, Jérôme O. 1 Ferretti, Claudio 1 Fried, Ervin 1 Gąsieniec, Leszek Antoni 1 Gibson, Donald Jason 1 Ginosar, Yuval 1 Goulden, Ian P. 1 Granville, Andrew James 1 Gruska, Jozef 1 Gumm, Heinz-Peter 1 Guo, Shuguang 1 Hatsuyama, Tomonobu 1 Henson, C. Ward 1 Huang, Yue 1 Imai, Katsunobu 1 Ionescu, Mihai 1 Ishdorj, Tseren-Onolt 1 Iwamoto, Chuzo 1 Ji, Hao 1 Kaarli, Kalle 1 Kaplan, Itay 1 Kellerer, Johann 1 Langer, Miroslav 1 Lemke Oliver, Robert J. 1 Leporati, Alberto 1 Levcopoulos, Christos 1 Li, Yaohang 1 Ling, Dan 1 Liu, Liucheng 1 Liu, Xiyu 1 Liu, Yijun 1 Lu, Chun 1 Luo, Xiaohui 1 Lv, Zeqiong 1 Margolis, Leo 1 Mascagni, Michael V. 1 Michel, Pascal 1 Mishina, A. P. 1 Morita, Kenichi 1 Moulin Ollagnier, Jean 1 Niskanen, Reino 1 Pagh, Rasmus 1 Pan, Tong 1 Pavel, Ana Brânduşa 1 Peitgen, Heinz-Otto 1 Persson, Mia 1 Pescini, Dario 1 Pixley, Alden F. 1 Potapov, Igor 1 Potra, Florian-Alexandru 1 Rajasekaran, Aayush ...and 37 more Authors
all top 5

#### Cited in 45 Serials

 21 Theoretical Computer Science 10 Mathematica Slovaca 5 Annals of Pure and Applied Logic 4 Algebra Universalis 3 Natural Computing 2 Discrete Applied Mathematics 2 Discrete Mathematics 2 The Journal of Symbolic Logic 2 Proceedings of the American Mathematical Society 2 European Journal of Combinatorics 2 International Journal of Foundations of Computer Science 2 Elemente der Mathematik 2 Archive for Mathematical Logic 2 Soft Computing 1 Acta Informatica 1 Archiv für Mathematische Logik und Grundlagenforschung 1 Information Processing Letters 1 Lithuanian Mathematical Journal 1 Mathematics of Computation 1 Beiträge zur Algebra und Geometrie 1 Czechoslovak Mathematical Journal 1 Journal of Computer and System Sciences 1 Journal of Number Theory 1 Journal of Soviet Mathematics 1 Topology and its Applications 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Algorithmica 1 Mathematical and Computer Modelling 1 Neural Networks 1 International Journal of Algebra and Computation 1 Bulletin of the American Mathematical Society. New Series 1 RAIRO. Informatique Théorique et Applications 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Experimental Mathematics 1 Tatra Mountains Mathematical Publications 1 Journal of Mathematical Sciences (New York) 1 Monte Carlo Methods and Applications 1 Complexity 1 Acta Mathematica et Informatica Universitatis Ostraviensis 1 The Ramanujan Journal 1 Theory of Computing Systems 1 Fundamenta Informaticae 1 Science China. Information Sciences 1 Computability 1 Journal of Membrane Computing
all top 5

#### Cited in 22 Fields

 51 Computer science (68-XX) 33 Number theory (11-XX) 17 Mathematical logic and foundations (03-XX) 7 General algebraic systems (08-XX) 6 Combinatorics (05-XX) 6 Group theory and generalizations (20-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Difference and functional equations (39-XX) 3 Numerical analysis (65-XX) 2 Field theory and polynomials (12-XX) 2 Special functions (33-XX) 2 Convex and discrete geometry (52-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Approximations and expansions (41-XX) 1 General topology (54-XX) 1 Statistics (62-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX)