arXiv subjects

J. Koppitz

Publications and source records attributed to J. Koppitz.

3 recordsLinked to original sources

arXiv2019

The rank of the inverse semigroup of partial automorphisms on a finite fence

A fence is a particular partial order on a (finite) set, close to the linear order. In this paper, we calculate the rank of the semigroup $\mathcal{FI}_{n}$ of all order-preserving partial injections on an $n$-element fence. In particular, we provide a minimal generating set for $\mathcal{FI}_{n}$. In the present paper, $n$ is odd since this problem for even $n$ was already solved by I. Dimitrova and J. Koppitz.

math.RA↗

arXiv2014

Stable varieties of semigroups and groupoids

The paper deals with $Σ-$composition and $Σ$-essential composition of terms, which lead to stable and s-stable varieties of algebras. A full description of all stable varieties of semigroups, commutative and idempotent groupoids is obtained. We use an abstract reduction system which simplifies the presentations of terms of type $τ=(2)$ to study the varietiy of idempotent groupoids and s-stable varieties of groupoids. They are used as an alternating of the stable varieties, aiming to highlight replacing the subterms of a term in a deductive systems instead of the usual replacing the variables with terms.

math.RA↗

arXiv2013

Finite symmetric functions with non-trivial arity gap

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 $f$. In the present paper we study the properties of the symmetric function with non-trivial arity gap ($2\leq gap(f)$). We prove several results concerning decomposition of the symmetric functions with non-trivial arity gap with its minors or subfunctions. We show that all non-empty sets of essential variables in symmetric functions with non-trivial arity gap are separable.

cs.DM↗