arXiv subjects

Elena Konstantinova

Publications and source records attributed to Elena Konstantinova.

4 recordsLinked to original sources

arXiv2018

$PI$-eigenfunctions of the Star graphs

We consider the symmetric group $\mathrm{Sym}_n,\,n\geqslant 2$, generated by the set $S$ of transpositions $(1~i),\,2 \leqslant i \leqslant n$, and the Cayley graph $S_n=Cay(\mathrm{Sym}_n,S)$ called the Star graph. For any positive integers $n\geqslant 3$ and $m$ with $n > 2m$, we present a family of $PI$-eigenfunctions of $S_n$ with eigenvalue $n-m-1$. We establish a connection of these functions with the standard basis of a Specht module. In the case of largest non-principal eigenvalue $n-2$ we prove that any eigenfunction of $S_n$ can be reconstructed by its values on the second neighbourhood of a vertex.

math.CO↗

arXiv2017

Physical Properties of the Spin Hamiltonian on Honeycomb Lattice Samples with Kekulé and Vacuum Polarization Corrections

Magnetic and thermodynamical properties of a system of spins in a honeycomb lattice, such as magnetization, magnetic susceptibility and specific heat, in a low-temperature regime are investigated by considering the effects of a Kekulé scalar exchange and QED vacuum polarization corrections to the interparticle potential. The spin lattice calculations are carried out by means of Monte Carlo simulations. We present a number of comparative plots of all the physical quantities we have considered and a detailed analysis is presented to illustrate the main features and the variation profiles of the properties with the applied external magnetic field and temperature.

cond-mat.mes-hall↗

arXiv2016

Scalar-Interchange Potential and Magnetic/Thermodynamic Properties of Graphene-like Materials

By means of numerical simulations, we explore possible effects of a special interparticle interaction potential which is a function of external and internal conditions of graphene-like systems. In addition to the electromagnetic interaction, we introduce a new potential due to the exchange of a massive scalar, associated to the so-called Kekulé deformations; this interaction displays a spin-dependent profile. It turns out that the magnitude of Kekulé deformation may significantly affect physical properties of graphene. A Monte Carlo analysis enables one to analyze the behavior of the system under variation of the applied external field, temperature, and the particular type of the exchanged excitation that induces the potential. We pursue an investigation of the spin configurations, we analyze differences in thermal equilibrium magnetization and we carry out calculations of the magnetic susceptibility and the specific heat in the presence of the Kekulé-induced new potential.

cond-mat.mes-hall↗

arXiv2007

Reconstruction of permutations distorted by single transposition errors

The reconstruction problem for permutations on $n$ elements from their erroneous patterns which are distorted by transpositions is presented in this paper. It is shown that for any $n \geq 3$ an unknown permutation is uniquely reconstructible from 4 distinct permutations at transposition distance at most one from the unknown permutation. The {\it transposition distance} between two permutations is defined as the least number of transpositions needed to transform one into the other. The proposed approach is based on the investigation of structural properties of a corresponding Cayley graph. In the case of at most two transposition errors it is shown that $\frac32(n-2)(n+1)$ erroneous patterns are required in order to reconstruct an unknown permutation. Similar results are obtained for two particular cases when permutations are distorted by given transpositions. These results confirm some bounds for regular graphs which are also presented in this paper.

math.CO↗