Standard

PI-eigenfunctions of the Star graphs. / Goryainov, Sergey; Kabanov, Vladislav; Konstantinova, Elena et al.

In: Linear Algebra and Its Applications, Vol. 586, 01.02.2020, p. 7-27.

Research output: Contribution to journal › Article › peer-review

Harvard

Goryainov, S, Kabanov, V, Konstantinova, E, Shalaginov, L & Valyuzhenich, A 2020, 'PI-eigenfunctions of the Star graphs', Linear Algebra and Its Applications, vol. 586, pp. 7-27. https://doi.org/10.1016/j.laa.2019.10.018

APA

Goryainov, S., Kabanov, V., Konstantinova, E., Shalaginov, L., & Valyuzhenich, A. (2020). PI-eigenfunctions of the Star graphs. Linear Algebra and Its Applications, 586, 7-27. https://doi.org/10.1016/j.laa.2019.10.018

Vancouver

Goryainov S, Kabanov V, Konstantinova E, Shalaginov L, Valyuzhenich A. PI-eigenfunctions of the Star graphs. Linear Algebra and Its Applications. 2020 Feb 1;586:7-27. doi: 10.1016/j.laa.2019.10.018

Author

Goryainov, Sergey ; Kabanov, Vladislav ; Konstantinova, Elena et al. / PI-eigenfunctions of the Star graphs. In: Linear Algebra and Its Applications. 2020 ; Vol. 586. pp. 7-27.

BibTeX

@article{46f995c9053c4176b648d395c799d150,
title = "PI-eigenfunctions of the Star graphs",
abstract = "We consider the symmetric group Symn, n⩾2, generated by the set S of transpositions (1i),2⩽i⩽n, and the Cayley graph Sn=Cay(Symn,S) called the Star graph. For any positive integers n⩾3 and m with n>2m, we present a family of eigenfunctions of Sn with eigenvalue n−m−1 and call them PI-eigenfunctions. We then establish a connection of these functions with the standard basis of a Specht module. Finally, in the case of the largest non-principal eigenvalue n−2 we prove that any eigenfunction of Sn can be reconstructed by its values on the second neighbourhood of a vertex.",
keywords = "Eigenfunction, Jucys-Murphy element, Polytabloid, Reconstruction, Specht module, Star graph, RECONSTRUCTION, CAYLEY-GRAPHS",
author = "Sergey Goryainov and Vladislav Kabanov and Elena Konstantinova and Leonid Shalaginov and Alexandr Valyuzhenich",
year = "2020",
month = feb,
day = "1",
doi = "10.1016/j.laa.2019.10.018",
language = "English",
volume = "586",
pages = "7--27",
journal = "Linear Algebra and Its Applications",
issn = "0024-3795",
publisher = "Elsevier Science Inc.",

}

RIS

TY - JOUR

T1 - PI-eigenfunctions of the Star graphs

AU - Goryainov, Sergey

AU - Kabanov, Vladislav

AU - Konstantinova, Elena

AU - Shalaginov, Leonid

AU - Valyuzhenich, Alexandr

PY - 2020/2/1

Y1 - 2020/2/1

N2 - We consider the symmetric group Symn, n⩾2, generated by the set S of transpositions (1i),2⩽i⩽n, and the Cayley graph Sn=Cay(Symn,S) called the Star graph. For any positive integers n⩾3 and m with n>2m, we present a family of eigenfunctions of Sn with eigenvalue n−m−1 and call them PI-eigenfunctions. We then establish a connection of these functions with the standard basis of a Specht module. Finally, in the case of the largest non-principal eigenvalue n−2 we prove that any eigenfunction of Sn can be reconstructed by its values on the second neighbourhood of a vertex.

AB - We consider the symmetric group Symn, n⩾2, generated by the set S of transpositions (1i),2⩽i⩽n, and the Cayley graph Sn=Cay(Symn,S) called the Star graph. For any positive integers n⩾3 and m with n>2m, we present a family of eigenfunctions of Sn with eigenvalue n−m−1 and call them PI-eigenfunctions. We then establish a connection of these functions with the standard basis of a Specht module. Finally, in the case of the largest non-principal eigenvalue n−2 we prove that any eigenfunction of Sn can be reconstructed by its values on the second neighbourhood of a vertex.

KW - Eigenfunction

KW - Jucys-Murphy element

KW - Polytabloid

KW - Reconstruction

KW - Specht module

KW - Star graph

KW - RECONSTRUCTION

KW - CAYLEY-GRAPHS

UR - http://www.scopus.com/inward/record.url?scp=85073606839&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2019.10.018

DO - 10.1016/j.laa.2019.10.018

M3 - Article

AN - SCOPUS:85073606839

VL - 586

SP - 7

EP - 27

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

ID: 21952803