Related papers: Upper bound of a band complex
Consider the configuration spaces of manifolds. We give a precise formula for the integral cohomological dimension (the degree of top non-trivial integral cohomology group) of unordered configuration spaces of manifolds with non-trivial…
A connected set in a graph is a subset of vertices whose induced subgraph is connected. Although counting the number of connected sets in a graph is generally a \#P-complete problem, it remains an active area of research. In 2020, Vince…
Capacity bounds for waveform channels under square-law detection of time-limited complex-valued signals are derived. The upper bound is the capacity of the channel under (complex-valued) coherent detection. The lower bound is one bit less,…
Recent studies on the interplay between band topology and layer degree of freedom provide an effective way to realize exotic topological phases. Here we systematically study the $C_6$- and $C_3$-symmetric higher-order topological phases in…
The band structure of alfa-(Per)2M(mnt)2, leads to a description of these materials as nearly perfectly one dimensional conductors. The conduction is mainly along the stacking direction of the partially oxidized perylene molecules,…
We prove that the invariably generating graph of a finite group can have an arbitrarily large number of connected components with at least two vertices.
Complex structures can only form in a universe that allows for bound states. While this is clearly observed in three-dimensions, added degrees of freedom in a higher-dimensional space preclude the immediate assumption that binding…
An upper bound on the capacity of multiple-input multiple-output (MIMO) Gaussian fading channels is derived under peak amplitude constraints. The upper bound is obtained borrowing concepts from convex geometry and it extends to MIMO…
We study the nucleation of crystalline cluster phases in the generalized exponential model with exponent n=4. Due to the finite value of this pair potential for zero separation, at high densities the system forms cluster crystals with…
Given a finite group $G$, the Engel graph of $G$ is a directed graph $\Gamma(G)$ encoding pairs of elements satisfying some Engel word. Namely, $\Gamma(G)$ is the directed graph, where the vertices are the non-hypercentral elements of $G$…
The first-principles band theory paradigm has been a key player not only in the process of discovering new classes of topologically interesting materials, but also for identifying salient characteristics of topological states, enabling…
Fiber bundles over infinite fields with non-trivial ultra-norms are considered. For them geometric wrap groups are defined and investigated. Besides fields also Cayley-Dickson algebras over fields of characteristic not equal to two are…
A number of recent articles have reported the existence of topologically non-trivial states and associated end states in one-dimensional incommensurate lattice models that would usually only be expected in higher dimensions. Using an…
The band structure of N=Z nuclei is constructed from intrinsic states defined in terms of quartets. The simplest of these states is a condensate of collective quartets with isospin T=0. The other intrinsic states are built by promoting one…
We tackle the problem of constructing increasing-chord graphs spanning point sets. We prove that, for every point set P with n points, there exists an increasing-chord planar graph with O(n) Steiner points spanning P. Further, we prove…
We investigate the unextendible maximally entangled bases in $\mathbb{C}^{d}\bigotimes\mathbb{C}^{d}$ and present a $30$-number UMEB construction in $\mathbb{C}^{6}\bigotimes\mathbb{C}^{6}$. For higher dimensional case, we show that for a…
We obtain an asymptotic upper bound for the product of the $p$-parts of the orders of certain composition factors of a finite group acting completely reducibly and faithfully on a finite vector space of order divisible by a prime $p$. An…
In Euclidean space there is a trivial upper bound on the maximum length of a compound "walk" built up of variable-length jumps, and a considerably less trivial lower bound on its minimum length. The existence of this non-trivial lower bound…
The recent discovery of topological insulators has revived interest in the topological properties of insulating band structures. In this work, we extend the topological classification of insulating band structures to include certain point…
We analyze site percolation on directed and undirected graphs with site-dependent open-site probabilities. We construct upper bounds on cluster susceptibilities, vertex connectivity functions, and the expected number of simple open cycles…