Related papers: Skein relations for spin networks, modified
Webs are planar graphs with boundary that describe morphisms in a diagrammatic representation category for $\mathfrak{sl}_k$. They are studied extensively by knot theorists because braiding maps provide a categorical way to express link…
As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…
In this paper, we characterize graphs with circular chromatic number less than 3 in terms of certain balancing labellings studied in the context of signed graphs. In fact, we construct a signed graph which is universal for all such…
Subgraph matching is vital in knowledge graph (KG) question answering, molecule design, scene graph, code and circuit search, etc. Neural methods have shown promising results for subgraph matching. Our study of recent systems suggests…
It is shown that the series of renormalon--type graphs, which consist in the chain of insertions to one soft(hard) gluon(photon) line is in fact ill defined. Each new type of insertions, which appears in the higher orders of perturbation…
We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another.…
We study curved-space rigid supersymmetry for two-dimensional $\mathcal{N}=(2,2)$ supersymmetric fields theories with a vector-like $R$-symmetry by coupling such theories to background supergravity. The associated Killing spinors can be…
We uncover the very rich graph topology of generic bounded non-Hermitian spectra, distinct from the topology of conventional band invariants and complex spectral winding. The graph configuration of complex spectra are characterized by the…
Self-assembly of chiral particles with an L-shape is explored by Monte-Carlo computer simulations in two spatial dimensions. For sufficiently high packing densities in confinement, a carpet-like texture emerges due to the interlocking of…
Coloured Alexander polynomials form a sequence of non-semisimple quantum invariants coming from the representation theory of the quantum group $U_q(sl(2))$ at roots of unity. This sequence recovers the original Alexander polynomial as the…
We present a family of networks, expanded deterministic Apollonian networks, which are a generalization of the Apollonian networks and are simultaneously scale-free, small-world, and highly clustered. We introduce a labeling of their…
The symmetry algebras of certain families of quantum spin chains are considered in detail. The simplest examples possess m states per site (m\geq2), with nearest-neighbor interactions with U(m) symmetry, under which the sites transform…
It was proposed in [(https://doi.org/10.1103/PhysRevLett.114.145301){Chen et al., Phys. Rev. Lett. $\mathbf{114}$, 145301 (2015)}] that spin-2 chains display an extended critical phase with enhanced SU$(3)$ symmetry. This hypothesis is…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
Combinatorial methods are developed to find the cluster coordinates for moduli space of flat connections which is describing the Coulomb branch of higher rank N=2 theories derived by compactifying six dimensional (2,0) theory on a punctured…
Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…
We characterise the quotient surface graphs arising from symmetric contact systems of line segments in the plane and also from symmetric pointed pseudotriangulations in the case where the group of symmetries is generated by a translation or…
The exact solution of a system of bilinear identities derived in the first part of our work [Nucl.Phys.A 938 (2015) 59] for the case of real Grassmann-odd tensor aggregate of the type $(S,V_{\mu},\!\,^{\ast}T_{\mu \nu},A_{\mu}, P)$ is…
We study classical spin networks with group SU(2). In the first part, using gaussian integrals, we compute their generating series in the case where the networks are equipped with holonomies; this generalizes Westbury's formula. In the…
Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bounds on the chromatic number of the graph via some of their…