# zbMATH — the first resource for mathematics

## Tyszka, Apoloniusz

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 Author ID: tyszka.apoloniusz Published as: Tyszka, A.; Tyszka, Apoloniusz
 Documents Indexed: 34 Publications since 1992 Reviewing Activity: 1 Review

#### Co-Authors

 32 single-authored 2 Sporysz, Maciej 1 Molenda, Krzysztof 1 Peszek, Agnieszka
all top 5

#### Serials

 7 Aequationes Mathematicae 6 Journal of Natural Geometry 4 International Mathematical Forum 2 Rocznik Naukowo-Dydaktyczny. Prace Matematyczne 1 American Mathematical Monthly 1 Information Processing Letters 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Collectanea Mathematica 1 Demonstratio Mathematica 1 Journal of Geometry 1 Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica 1 Mathematical Logic Quarterly (MLQ) 1 Analele Ştiinţifice ale Universităţii “Ovidius” Constanţa. Seria: Matematică 1 Fundamenta Informaticae 1 Acta Mathematica Academiae Paedagogicae Nyíregyháziensis. New Series 1 Nonlinear Functional Analysis and Applications 1 Forum Geometricorum
all top 5

#### Fields

 15 Mathematical logic and foundations (03-XX) 14 Geometry (51-XX) 7 Number theory (11-XX) 6 Combinatorics (05-XX) 4 Field theory and polynomials (12-XX) 2 Algebraic geometry (14-XX) 2 Category theory; homological algebra (18-XX) 2 Difference and functional equations (39-XX) 2 Convex and discrete geometry (52-XX) 1 General algebraic systems (08-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX)

#### Citations contained in zbMATH

11 Publications have been cited 13 times in 8 Documents Cited by Year
Does there exist an algorithm which to each Diophantine equation assigns an integer which is greater than the modulus of integer solutions, if these solutions form a finite set? Zbl 1288.11116
Tyszka, Apoloniusz
2013
Beckman-Quarles type theorems for mappings from $$\mathbb{R}^n$$ to $$\mathbb{C}^n$$. Zbl 1054.51011
Tyszka, Apoloniusz
2004
Conjecturally computable functions which unconditionally do not have any finite-fold Diophantine representation. Zbl 1285.11147
Tyszka, Apoloniusz
2013
A conjecture on integer arithmetic which implies that there is an algorithm which to each Diophantine equation assigns an integer which is greater than the heights of integer (non-negative integer, rational) solutions, if these solutions form a finite set. Zbl 1301.11080
Tyszka, Apoloniusz; Sporysz, Maciej; Peszek, Agnieszka
2013
An algorithm which transforms any Diophantine equation into an equivalent system of equations of the forms $$x_i=1$$, $$x_i+x_j=x_k$$, $$x_i \cdot x_j=x_k$$. Zbl 1285.11150
Tyszka, Apoloniusz; Molenda, Krzysztof; Sporysz, Maciej
2013
Some conjectures on addition and multiplication of complex (real) numbers. Zbl 1239.12002
Tyszka, Apoloniusz
2009
A discrete form of the Beckman-Quarles theorem for mappings from $$\mathbb{R}^2\,(\mathbb{C}^2)$$ to $$\mathbb{F}^2$$, where $$\mathbb{F}$$ is a subfield of a commutative field extending $$\mathbb{R}\,(\mathbb{C})$$. Zbl 1106.51007
Tyszka, Apoloniusz
2006
A discrete form of the Beckman-Quarles theorem for two-dimensional strictly convex normed spaces. Zbl 1034.46021
Tyszka, Apoloniusz
2002
On binary relations without non-identical endomorphisms. Zbl 1002.03040
Tyszka, Apoloniusz
2002
Discrete versions of the Beckman-Quarles theorem. Zbl 0948.51014
Tyszka, Apoloniusz
2000
On the notion of a geometric object in a Klein space. Zbl 0803.18006
Tyszka, Apoloniusz
1993
Does there exist an algorithm which to each Diophantine equation assigns an integer which is greater than the modulus of integer solutions, if these solutions form a finite set? Zbl 1288.11116
Tyszka, Apoloniusz
2013
Conjecturally computable functions which unconditionally do not have any finite-fold Diophantine representation. Zbl 1285.11147
Tyszka, Apoloniusz
2013
A conjecture on integer arithmetic which implies that there is an algorithm which to each Diophantine equation assigns an integer which is greater than the heights of integer (non-negative integer, rational) solutions, if these solutions form a finite set. Zbl 1301.11080
Tyszka, Apoloniusz; Sporysz, Maciej; Peszek, Agnieszka
2013
An algorithm which transforms any Diophantine equation into an equivalent system of equations of the forms $$x_i=1$$, $$x_i+x_j=x_k$$, $$x_i \cdot x_j=x_k$$. Zbl 1285.11150
Tyszka, Apoloniusz; Molenda, Krzysztof; Sporysz, Maciej
2013
Some conjectures on addition and multiplication of complex (real) numbers. Zbl 1239.12002
Tyszka, Apoloniusz
2009
A discrete form of the Beckman-Quarles theorem for mappings from $$\mathbb{R}^2\,(\mathbb{C}^2)$$ to $$\mathbb{F}^2$$, where $$\mathbb{F}$$ is a subfield of a commutative field extending $$\mathbb{R}\,(\mathbb{C})$$. Zbl 1106.51007
Tyszka, Apoloniusz
2006
Beckman-Quarles type theorems for mappings from $$\mathbb{R}^n$$ to $$\mathbb{C}^n$$. Zbl 1054.51011
Tyszka, Apoloniusz
2004
A discrete form of the Beckman-Quarles theorem for two-dimensional strictly convex normed spaces. Zbl 1034.46021
Tyszka, Apoloniusz
2002
On binary relations without non-identical endomorphisms. Zbl 1002.03040
Tyszka, Apoloniusz
2002
Discrete versions of the Beckman-Quarles theorem. Zbl 0948.51014
Tyszka, Apoloniusz
2000
On the notion of a geometric object in a Klein space. Zbl 0803.18006
Tyszka, Apoloniusz
1993

#### Cited by 4 Authors

 4 Tyszka, Apoloniusz 2 Gehér, György Pál 1 Kuzminykh, Alexandr V. 1 Moszner, Zenon
all top 5

#### Cited in 6 Serials

 2 Aequationes Mathematicae 1 Information Processing Letters 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Journal of Geometry 1 Linear Algebra and its Applications 1 Mathematical Logic Quarterly (MLQ)
all top 5

#### Cited in 9 Fields

 3 Mathematical logic and foundations (03-XX) 3 Number theory (11-XX) 2 Functional analysis (46-XX) 2 Geometry (51-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Difference and functional equations (39-XX) 1 Convex and discrete geometry (52-XX)