Related papers: The Effect of Symmetry-preserving Operations on 3-…
Lopsp-operations are operations on maps that are applied locally and are guaranteed to preserve all the orientation-preserving symmetries of maps. Well-known examples of such operations are dual, ambo, truncation, and leapfrog. They are…
Unifying approaches by amongst others Archimedes, Kepler, Goldberg, Caspar and Klug, Coxeter, and Conway, and extending on a previous formalisation of the concept of local symmetry preserving (lsp) operations, we introduce a formal…
We prove that local operations that preserve all symmetries, as e.g. dual, truncation, ambo, or join,, as well as local operations that preserve all symmetries except orientation reversing ones, as e.g. gyro or snub, preserve the…
We introduce a new practical and more general definition of local symmetry-preserving operations on polyhedra. These can be applied to arbitrary plane graphs and result in plane graphs with the same symmetry. With some additional properties…
In this article we investigate the question which local symmetry preserving operations can not only preserve, but also increase the symmetry of a polyhedral map. Often operations that can increase symmetry, can nevertheless not do so for…
We consider the class of semi-transitively orientable graphs, which is a much larger class of graphs compared to transitively orientable graphs, in other words, comparability graphs. Ever since the concept of a semi-transitive orientation…
In this paper, we give the complete description of maps on self-adjoint bounded operators on Hilbert space which preserve a triadic relation involving the difference of operators and either commutativity or quasi-commutativity in both…
This paper describes a characterization of tightness of closed contact 3-manifolds in terms of supporting open book decompositions. The main result is that tightness of a closed contact 3-manifold is preserved under Legendrian surgery.
There are operations that transform a map M (an embedding of a graph on a surface) into another map in the same surface, modifying its structure and consequently its set of flags F(M). For instance, by truncating all the vertices of a map…
This paper presents a hybrid algorithm that combines features form both Sqrt(3) and Loop Subdivision schemes. The algorithm aims at preserving sharp features and trim regions, during the surfaces subdivision, using a set of rules. The…
We contribute to the theory for minimal liftings of cut-generating functions. In particular, we give three operations that preserve the so-called covering property of certain structured cut-generating functions. This has the consequence of…
In this paper, we study the construction and transformation of two-dimensional persistent graphs. Persistence is a generalization to directed graphs of the undirected notion of rigidity. In the context of moving autonomous agent formations,…
In this partly expository paper we discuss and describe some of our old and recent results on partial orders on the set (m,n)-graphs (i.e. graphs with n vertices and m edges) and some operations on graphs that are monotone with respect to…
B\'erczi, Chandrasekaran, Kir\'aly, and Kulkarni (ICALP 2024) recently described a splitting-off procedure in hypergraphs that preserves local-connectivity and outlined some applications. In this note we give an alternative proof via…
It is shown that for any locally knotted edge of a 3-connected graph in $S^3$, there is a ball that contains all of the local knots of that edge and is unique up to an isotopy setwise fixing the graph. This result is applied to the study of…
We show how to construct embedding space three-point functions for operators in arbitrary Lorentz representations by employing the formalism developed in arXiv:1905.00036 and arXiv:1905.00434. We study tensor structures that intertwine the…
An ordered and oriented 2-component link L in the 3-sphere is said to be achiral if it is ambient isotopic to its mirror image ignoring the orientation and ordering of the components. Kirk-Livingston showed that if L is achiral then the…
We describe a model $\mathcal{M}_3^{comb}$ for the boundary of the connectedness locus $\mathcal{M}^{sy}_3$ of the parameter space of cubic symmetric polynomials $p_c(z)=z^3-3c^2z$. We show that there exists a monotone continuous function…
Flip graphs of combinatorial and geometric objects are at the heart of many deep structural insights and connections between different branches of discrete mathematics and computer science. They also provide a natural framework for the…
The splitting-off operation in undirected graphs is a fundamental reduction operation that detaches all edges incident to a given vertex and adds new edges between the neighbors of that vertex while preserving their degrees. Lov\'asz (1974)…