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Given an n-ary k-valued function f , gap(f) denotes the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f . We particularly solve a problem concerning the explicit determination of n-ary k-valued functions f with 2 ≤ gap(f) ≤ n ≤ k. Our methods yield new combinatorial results about the… (More)

- Klaus Denecke, Jörg Koppitz, Slavcho Shtrakov
- Journal of Automata, Languages and Combinatorics
- 2001

- Klaus Denecke, Jörg Koppitz, Slavcho Shtrakov
- IJAC
- 2006

Hypersubstitutions are mappings which map operation symbols to terms. Terms can be visualized by trees. Hypersubstitutions can be extended to mappings defined on sets of trees. The nodes of the trees, describing terms, are labelled by operation symbols and by colors, i.e. certain positive integers. We are interested in mappings which map differently colored… (More)

- Sl. Shtrakov, Jörg Koppitz
- 2010

Given an n-ary k−valued function f , gap(f) denotes the essential arity gap of f which is the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f . The class G p,k of all n-ary k−valued functions f with 2 ≤ gap(f) is explicitly determined by the authors and R. Willard in [5, 7, 8]. We… (More)

We consider groups as algebras of type (2, 1, 0). A hypersubstitution of type (2, 1, 0) is a mapping σ from the set of the operation symbols {·,−1 , e} into the set of terms of type (2, 1, 0) preserving the arity. For a monoid M of hypersubstitutions of type (2, 1, 0) a variety V is called M -solid if for each group (G; ·,−1 , e) ∈ V the derived group (G;… (More)

- Klaus Denecke, Jörg Koppitz, Staszek Niwczyk
- IJAC
- 2002

- Klaus Denecke, Jörg Koppitz, SL . SHTRAKOV
- 2009

Hypersubstitutions are mappings which map operation symbols to terms. Terms can be visualized by trees. Hypersubstitutions can be extended to mappings defined on sets of trees. The nodes of the trees, describing terms, are labelled by operation symbols and by colors, i.e. certain positive integers. We are interested in mappings which map differently colored… (More)

- Klaus Denecke, Jörg Koppitz, R. Marszalek
- IJAC
- 1998

We study the structure of the ideals of the semigroup IOn of all isotone (order-preserving) partial injections as well as of the semigroup IMn of all monotone (order-preserving or order-reversing) partial injections on an n-element set. The main result is the characterization of the maximal subsemigroups of the ideals of IOn and IMn.

The extensions of hypersubstitutions are mappings on the set of all terms. In the present paper we characterize all hypersubstitutions which provide bijections on the set of all terms. The set of all such hypersubstitutions forms a monoid. On the other hand, one can modify each hypersubstitution to any mapping on the set of terms. For this we can consider… (More)