arXiv subjects

Jörg Koppitz

Publications and source records attributed to Jörg Koppitz.

22 records · Page 2Linked to original sources

arXiv2020

Generating Sets of an Infinite Semigroup of Transformations Preserving a Zig-zag Order

A zig-zag order is like a directed path, only with alternating directions. A generating set of minimal size for the semigroup of all full transformations on a finite set preserving the zig-zag order was determined by Fenandes et al. in 2019. This paper deals with generating sets of the semigroup $F_{\mathbb{N}}$ of all full transformations on the set of all natural numbers preserving the zig-zag order. We prove that $F_{\mathbb{N}}$ has no minimal generating sets and present two particular infinite decreasing chains of generating sets of $F_{\mathbb{N}}$.

math.RA↗

arXiv2020

On relative ranks of finite transformation semigroups with restricted range

In this paper, we determine the relative rank of the semigroup $T(X,Y)$ of all transformations on a finite chain $X$ with restricted range $Y \subseteq X$ modulo the set $OP(X,Y)$ of all orientation-preserving transformation in $T(X,Y)$. Moreover, we state the relative rank of the semigroup $OP(X,Y)$ modulo the set $O(X,Y)$ of all order-preserving transformations in $OP(X,Y)$. In both cases we characterize the minimal relative generating sets.

math.RA↗

arXiv2018

Ranks of monoids of endomorphisms of a finite undirected path

In this paper we study the widely considered endomorphisms and weak endomorphisms of a finite undirected path from monoid generators perspective. Our main aim is to determine the ranks of the monoids $wEnd P_n$ and $End P_n$ of all weak endomorphisms and all endomorphisms of the undirected path $P_n$ with $n$ vertices. We also consider strong and strong weak endomorphisms of $P_n$.

math.RA↗

arXiv2015

A note on generators of the endomorphism semigroup of an infinite countable chain

In this note, we consider the semigroup $O(X)$ of all order endomorphisms of an infinite chain $X$ and the subset $J$ of $O(X)$ of all transformations $α$ such that $|Im(α)|=|X|$. For an infinite countable chain $X$, we give a necessary and sufficient condition on $X$ for $O(X) = \langle J \rangle$ to hold. We also present a sufficient condition on $X$ for $O(X) = \langle J \rangle$ to hold, for an arbitrary infinite chain $X$.

math.RA↗