Related papers: On spectral sets of integers
For $l,n \in \mathbb{N}$ we define tonal partition algebra $P^l_n$ over $\mathbb{Z}[\delta]$. We construct modules $\{ \Delta_{\underline{\mu}} \}_{\underline{\mu}}$ for $P^l_n$ over $\mathbb{Z}[\delta]$, and hence over any integral domain…
A "spectral convex set" is a collection of symmetric matrices whose range of eigenvalues form a symmetric convex set. Spectral convex sets generalize the Schur-Horn orbitopes studied by Sanyal-Sottile-Sturmfels (2011). We study this class…
If a finite set $A$ tiles the integers by translations, it also admits a tiling whose period $M$ has the same prime factors as $|A|$. We prove that the minimal period of such a tiling is bounded by $\exp(c(\log D)^2/\log\log D)$, where $D$…
In this short note, we give basic enumerative results on colored integer partitions.
In this paper, we give a geometric construction of string algebras and of their module categories. Our approach uses dissections of punctured Riemann surfaces with extra data at marked points, called labels. As an application, we give a…
We use spectral theory to produce embeddings of distributions in the algebras of generalized functions on a closed Riemannian manifold. These embeddings are invariant under isometries and preserve the singularity structure of the…
The random networks enriched with additional structures as metric and group-symmetry in background metric space are investigated. The important quantities like he clustering coefficient as well as the mean degree of separation in such…
This review presents an account of the major works done on spectra of adjacency matrices drawn on networks and the basic understanding attained so far. We have divided the review under three sections: (a) extremal eigenvalues, (b) bulk part…
In this paper, we investigate the Moore-Penrose inversion of a simple connected graph. We analyze qualitative, statistical, and extreme properties of spectral indices of signable pseudo-invertible graphs. We introduce and analyze a wide…
We prove the generic existence of spectral networks for a large class of spectral data.
In our article we consider some algebraical methods which may be useful in some inverse spectral problems. The reconstraction of the matrix from its minors is considered.
Using the index theory of seaweed algebras, we explore various new integer partition statistics. We find relations to some well-known varieties of integer partitions as well as a surprising periodicity result.
In this paper, we study a particular class of block matrices placing an emphasis on their spectral properties. Some related applications are then presented.
Assumed to be undirected, simple, and connected are all of the graphs in this study, and adjacency matrix $A$ serves as the associated matrix. In this paper we show that it is possible to relate a creation sequence for a type of cographs…
This is a survey on spectral theory of dynamical systems.
Inter alia, we present a Fourier series involving the generalised Stieltjes constants.
A concise overview of the spectral theory of integral-functional operators is provided. In the context of analysis, a technique is described for deriving solutions to equations involving operators in a closed form. A constructive theorem…
A brief summary on the properties of the so called Joint Spectral Radius
Curious spectral properties of an ensemble of random unitary matrices appearing in the quantization of a map p -> p+alpha, q -> q+f(p+alpha) in [Giraud et al. nlin.CD/0403033] are investigated. When alpha=m/n with integer co-prime m,n and…
We consider the joint distribution of the area and perimeter statistics on the set I_n of inversion sequences of length n represented as bargraphs. Functional equations for both the ordinary and exponential generating functions are derived…