Karsten Schölzel
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Karsten Schölzel has a total of 10 co-authors. Here are the top co-authors by number of shared publications:
- Miguel Couceiro
INESC-ID, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal
11 shared publications - Erkko Lehtonen
Institut für Algebra, Technische Universität Dresden, Dresden, Germany
6 shared publications Lucien Haddad
5 shared publications- Tamás Waldhauser
Bolyai Institute, University of Szeged, Szeged, Hungary
3 shared publications - Lucien Haddad
Royal Military College of Canada, Ontario, Canada
2 shared publications Boris A. Romov
1 shared publication
Latest Publications
- 1 May 2017
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 82-87
On the Nonexistence of Minimal Strong Partial Clones
Let k be a k-element set. We show that the lattice of all strong partial clones on k has no minimal elements. Moreover, we show that if C is a strong partial clone, then the family of all partial subclones of C is of continuum cardinality. We also show that in almost all cases, every strong partial clone contains a family of continuum cardinality of strong partial subclones.
- 1 May 2017
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 82-87
On the Nonexistence of Minimal Strong Partial Clones
Let k be a k-element set. We show that the lattice of all strong partial clones on k has no minimal elements. Moreover, we show that if C is a strong partial clone, then the family of all partial subclones of C is of continuum cardinality. We also show that in almost all cases, every strong partial clone contains a family of continuum cardinality of strong partial subclones.
- 6 January 2017
- Published by Springer Nature in Algebra universalis
- Vol. 77 (1) , 101-123
On the interval of strong partial clones of Boolean functions containing Pol({(0, 0), (0, 1), (1, 0)})- 6 January 2017
- Published by Springer Nature in Algebra universalis
- Vol. 77 (1) , 101-123
On the interval of strong partial clones of Boolean functions containing Pol({(0, 0), (0, 1), (1, 0)})- 5 August 2015
- Published by Springer Nature in Aequationes mathematicae
- Vol. 90 (2) , 411-425
Power series solutions of Tarski’s associativity law and of the cyclic associativity law
- 5 August 2015
- Published by Springer Nature in Aequationes mathematicae
- Vol. 90 (2) , 411-425
Power series solutions of Tarski’s associativity law and of the cyclic associativity law
- Open Access
Hereditarily rigid relations
An $h$-ary relation $\r$ on a finite set $A$ is said to be \emph{hereditarily rigid} if the unary partial functions on $A$ that preserve $\r$ are the subfunctions of the identity map or of constant maps. A family of relations ${\mathcal F}$ is said to be \emph{hereditarily strongly rigid} if the partial functions on $A$ that preserve every $\r \in {\mathcal F}$ are the subfunctions of projections or constant functions. In this paper we show that hereditarily rigid relations exist and we give a lower bound on their arities. We also prove that no finite hereditarily strongly rigid families of relations exist and we also construct an infinite hereditarily strongly rigid family of relations.Open AccessHereditarily rigid relations
An $h$-ary relation $\r$ on a finite set $A$ is said to be \emph{hereditarily rigid} if the unary partial functions on $A$ that preserve $\r$ are the subfunctions of the identity map or of constant maps. A family of relations ${\mathcal F}$ is said to be \emph{hereditarily strongly rigid} if the partial functions on $A$ that preserve every $\r \in {\mathcal F}$ are the subfunctions of projections or constant functions. In this paper we show that hereditarily rigid relations exist and we give a lower bound on their arities. We also prove that no finite hereditarily strongly rigid families of relations exist and we also construct an infinite hereditarily strongly rigid family of relations. - 1 May 2015
- Published by Elsevier in Discrete Applied Mathematics
- Vol. 187, 12-18
Set-reconstructibility of Post classes
- 1 May 2015
- Published by Elsevier in Discrete Applied Mathematics
- Vol. 187, 12-18
Set-reconstructibility of Post classes
- 29 April 2015
- Published by Springer Nature in Algebra universalis
- Vol. 73 (3-4) , 347-368
Dichotomy on intervals of strong partial Boolean clones
- 29 April 2015
- Published by Springer Nature in Algebra universalis
- Vol. 73 (3-4) , 347-368
Dichotomy on intervals of strong partial Boolean clones
- 17 December 2014
- Published by EDP Sciences in RAIRO - Operations Research
- Vol. 49 (1) , 39-66
A complete classification of equational classes of threshold functions included in clones
The class of threshold functions is known to be characterizable by functional equations or, equivalently, by pairs of relations, which are called relational constraints. It was shown by Hellerstein that this class cannot be characterized by a finite number of such objects. In this paper, we investigate classes of threshold functions which arise as intersections of the class of all threshold functions with clones of Boolean functions, and provide a complete classification of such intersections in respect to whether they have finite characterizations. Moreover, we provide a characterizing set of relational constraints for each class of threshold functions arising in this way.
- 17 December 2014
- Published by EDP Sciences in RAIRO - Operations Research
- Vol. 49 (1) , 39-66
A complete classification of equational classes of threshold functions included in clones
The class of threshold functions is known to be characterizable by functional equations or, equivalently, by pairs of relations, which are called relational constraints. It was shown by Hellerstein that this class cannot be characterized by a finite number of such objects. In this paper, we investigate classes of threshold functions which arise as intersections of the class of all threshold functions with clones of Boolean functions, and provide a complete classification of such intersections in respect to whether they have finite characterizations. Moreover, we provide a characterizing set of relational constraints for each class of threshold functions arising in this way.
- 4 July 2014
- Published by Springer Nature in Order
- Vol. 32 (2) , 255-292
Hypomorphic Sperner Systems and Non-Reconstructible Functions
- 4 July 2014
- Published by Springer Nature in Order
- Vol. 32 (2) , 255-292
Hypomorphic Sperner Systems and Non-Reconstructible Functions
- 1 May 2014
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 161-166
Relation Graphs and Partial Clones on a 2-Element Set
In a recent paper, the authors show that the sublattice of partial clones that preserve the relation {(0,0),(0,1),(1,0)} is of continuum cardinality on 2. In this paper we give an alternative proof to this result by making use of a representation of relations derived from {(0,0),(0,1),(1,0)} in terms of certain types of graphs. As a by-product, this tool brings some light into the understanding of the structure of this uncountable sublattice of strong partial clones.
- 1 May 2014
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 161-166
Relation Graphs and Partial Clones on a 2-Element Set
In a recent paper, the authors show that the sublattice of partial clones that preserve the relation {(0,0),(0,1),(1,0)} is of continuum cardinality on 2. In this paper we give an alternative proof to this result by making use of a representation of relations derived from {(0,0),(0,1),(1,0)} in terms of certain types of graphs. As a by-product, this tool brings some light into the understanding of the structure of this uncountable sublattice of strong partial clones.
- 1 May 2014
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- No. 0195623X,p. 91-96
Partial R-Clones
In [11] the first author introduced a type of partial clones as the intersection of some special infinite descending chains similar to I. Rosenberg [12] in the case of total clones. We provide a characterization of these clones in terms of their invariants, and propose a generalization of such clones, which we call partial R-clones. We show that there are only finitely many partial R-clones. Furthermore, we investigate some properties related to their position in the lattice of partial clones.
- 1 May 2014
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- No. 0195623X,p. 91-96
Partial R-Clones
In [11] the first author introduced a type of partial clones as the intersection of some special infinite descending chains similar to I. Rosenberg [12] in the case of total clones. We provide a characterization of these clones in terms of their invariants, and propose a generalization of such clones, which we call partial R-clones. We show that there are only finitely many partial R-clones. Furthermore, we investigate some properties related to their position in the lattice of partial clones.