Related papers: Spindle Starshaped Sets
To a set $\mathcal{B}$ of 4-subsets of a set $\Omega$ of size $n$ we introduce an invariant called the `hole stabilizer' which generalises a construction of Conway, Elkies and Martin of the Mathieu group $M_{12}$ based on Loyd's…
Packings of identical objects have fascinated both scientists and laymen alike for centuries, in particular the sphere packings and the packings of identical regular tetrahedra. Mathematicians have tried for centuries to determine the…
Are there examples of "astrophysical Russian dolls," and what could we learn from their similarities? In this article, we list a few such examples, including disks, filaments, and clusters. We suggest that forging connections across…
We consider projection and lifting of labelled galleries to and from roots subsystems. Our constructions allow us to construct some topological embeddings of Bott-Samelson varieties skew equivariant with respect to the compact torus and…
Various spectral notions have been employed to grasp the structure of point sets, in particular non-periodic ones. In this article, we present them in a unified setting and explain the relations between them. For the sake of readability, we…
We focus our attention on well-covered graphs that are vertex decomposable. We show that for many known families of these vertex decomposable graphs, the set of shedding vertices forms a dominating set. We then construct three new infinite…
This paper investigates the linear response of a series of spheroidal stellar clusters, the Kuzmin-Kutuzov St\"ackel family, which exhibit a continuous range of flattening and rotation, extending from an isochrone sphere to a Toomre disk.…
The notion of a simplicial set originated in algebraic topology, and has also been utilized extensively in category theory, but until relatively recently was not used outside of those fields. However, with the increasing prominence of…
This is an investigation of the role of shuffling and concatenating in the theory of graph drawing. A simple syntactic description of these and related operations is proved complete in the context of finite partial orders, as general as…
Many aspects concerning the formation of spiral and disc galaxies remain unresolved, despite their discovery and detailed study over the past $150$ years. As such, we present the results of an observational search for proto-spiral galaxies…
We list classical spherical subalgebras in basic matrix Lie superalgebras which are quantizable to coideal subalgebras in the standard quantum supergroups, for any choice of Borel subalgebra. We classify the corresponding Satake-type…
This paper addresses the questions of what we have learned about how and when dense star clusters form, and what studies of star clusters have revealed about galaxy formation and evolution. One important observation is that globular…
This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to…
This article defines a new family of curves in space, whose graphs generate shapes similar to whirls. An intrinsic equation is found, in terms of curvature and torsion, which gives necessary and sufficient conditions for the existence of…
Accumulation of new data on stellar hierarchical systems and the progress in numerical simulations of their formation open the door to genetic classification of these systems, where properties of a certain group (family) of objects are…
In spite of the almost all-encompassing variability of Be stars, surveys play a steadily increasing role in complementing the insights gained from single-star studies. The definition of classical Be stars as recently augmented by…
In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs. In the first paper of our series we determined structures that are complementary to arbitrary…
We extend so-called slit-slide-sew bijections to constellations and quasiconstellations. We present an involution on the set of hypermaps given with an orientation, one distinguished corner, and one distinguished edge leading away from the…
In this paper, we introduce twisted virtual doodles, defined as stable equivalence classes of immersed circles on closed surfaces that may be non-orientable. These objects admit planar representative diagrams, considered up to a suitable…
Recent JWST observations have revealed the prevalence of spiral structures at $z > 1$. Unlike in the local Universe, the origin and the consequence of spirals at this epoch remain unexplored. We use public JWST/NIRCam data from the…