We characterise the respective semigroups of mappings that preserve, or that preserve or
reverse orientation of a finite cycle, in terms of their actions on oriented triples and oriented …

An ordered matching of size $ n $ is a graph on a linearly ordered vertex set $ V $, $| V|= 2n
$, consisting of $ n $ pairwise disjoint edges. There are three different ordered matchings of …

A barcode is a finite multiset of closed intervals on the real line. Barcodes are important
objects in topological data analysis, where they serve as summaries of the persistent …

A\emph {square} is a word of the form $ UU $, where $ U $ is any finite nonempty word. For
instance, $\mathtt {\color {red}{0102}\color {blue}{0102}} $ is a square. A\emph {shuffle …

Two recent publications describe realizable Gauss diagrams using conditions stating that
the number of chords in certain sets of chords is even or odd. We demonstrate that these …

Chord diagrams, under the name of Gauss diagrams, are used in low-dimensional topology
as an important tool for studying curves or knots. Those Gauss diagrams that correspond to …

Gauss diagrams, or more generally chord diagrams are a well-established tool in the study
of topology of knots and of planar curves. In this paper we present a system description of …

Recent research in computational topology found sets of counterexamples demonstrating
that several recent mathematical articles purporting to describe a mathematical concept of …

A double occurrence word (DOW) is a word in which every symbol appears exactly twice;
two DOWs are equivalent if one is a symbol-to-symbol image of the other. We consider the …

A Gauss diagram (or, more generally, a chord diagram) consists of a circle and some chords
inside it. Gauss diagrams are a well-established tool in the study of topology of knots and of …