Related papers: Rack shadows and their invariants
A rainbow stacking of $r$-edge-colorings $\chi_1, \ldots, \chi_m$ of the complete graph on $n$ vertices is a way of superimposing $\chi_1, \ldots, \chi_m$ so that no edges of the same color are superimposed on each other. We determine a…
This paper studies the chirality of knotoids using shadow quandle colorings and the shadow quandle cocycle invariant. The shadow coloring number and the shadow quandle cocycle invariant is shown to distinguish infinitely many knotoids from…
3D reconstruction is a fundamental problem in computer vision, and the task is especially challenging when the object to reconstruct is partially or fully occluded. We introduce a method that uses the shadows cast by an unobserved object in…
A spatial surface is a compact surface embedded in the 3-sphere. In this paper, we provide several typical examples of spatial surfaces and construct a coloring invariant to distinguish them. The coloring is defined by using a multiple…
Classical shadows are an efficient method for constructing an approximate classical description of a quantum state using very few measurements. In the paper we propose to enhance classical shadow methods using bootstrap resampling methods.…
We introduce an infinite family of quantum enhancements of the biquandle counting invariant we call biquandle virtual brackets. Defined in terms of skein invariants of biquandle colored oriented knot and link diagrams with values in a…
Path-addition is an operation that takes a graph and adds an internally vertex-disjoint path between two vertices together with a set of supplementary edges. Path-additions are just the opposite of taking minors. We show that some classes…
A natural oriented (2k+2)-chain in CP^{2k+1} with boundary twice RP^{2k+1}, its complex shade, is constructed. Via intersection numbers with the shade, a new invariant, the shade number of k-dimensional subvarieties with normal vector…
Racks do not give us invariants of surface-knots in general. For example, if a surface-knot diagram has branch points (and a rack which we use satisfies some mild condition), then it admits no rack colorings. In this paper, we investigate…
$O(N)$ invariants are the observables of real tensor models. We use regular colored graphs to represent these invariants, the valence of the vertices of the graphs relates to the tensor rank. We enumerate $O(N)$ invariants as $d$-regular…
In 1993, Fenn, Rourke and Sanderson introduced rack spaces and rack homotopy invariants, and modifications to quandle spaces and quandle homotopy invariants were introduced by Nosaka in 2011. In this paper, we define the Cayley-type graph…
In any CAT(k) space M, the "shadow" of a tangent vector Z at a point p is the set vectors that form an angle of \pi or more with Z. Taking logarithm maps at points approaching p along a fixed geodesic ray from p with tangent Z collapses the…
We define a new topological invariant of line arrangements in the complex projective plane. This invariant is a root of unity defined under some combinatorial restrictions for arrangements endowed with some special torsion character on the…
A "shadow" of a subset $S$ of Euclidean space is an orthogonal projection of $S$ into one of the coordinate hyperplanes. In this paper we show that it is not possible for all three shadows of a cycle (i.e., a simple closed curve) in…
In this article, we investigate the relationship between the shadowing property of set-valued maps and their associated inverse limit systems. We show that if a set-valued map is expansive and open in the context of set-valued dynamics,…
Spectrahedral shadows are projections of linear sections of the cone of positive semidefinite matrices. We characterize the polynomials that vanish on the boundaries of these convex sets when both the section and the projection are generic.
Consider a $k$-valued network. Two kinds of (control) invariant subspaces, called state and dual invariant subspaces, are proposed, which are subspaces of state space and dual space respectively. Algorithms are presented to verify whether a…
We define a fat staircase to be a Ferrers diagram corresponding to a partition of the form $(n^{\alpha_n}, {n-1}^{\alpha_{n-1}},..., 1^{\alpha_1})$, where $\alpha = (\alpha_1,...,\alpha_n)$ is a composition, or the $180^\circ$ rotation of…
Shadows encode rich information about scene geometry and illumination, yet existing methods either predict a unified shadow mask or overlook attached shadows entirely. We address this gap by proposing a framework for jointly detecting cast…
An alternative framework underlying connection between tensor ${\rm sl}_2$-calculus and spin networks is suggested. New sign convention for the inner product in the dual spinor space leads to a simpler and direct set of initial rules for…