TY - JOUR

T1 - CONSTRUCTING SEGMENTS OF QUADRATIC LENGTH IN Spec(Tn) THROUGH SEGMENTS OF LINEAR LENGTH

AU - Kravchuk, A. V.

N1 - The work is supported by the Mathematical Center in Akademgorodok, under agreement No. 075-15-2022-281 with the Ministry of Science and High Education of the Russian Federation.

PY - 2024/1/1

Y1 - 2024/1/1

N2 - A Transposition graph Tn is defined as a Cayley graph over the symmetric group Symn generated by all transpositions. It is known that the spectrum of Tn consists of integers, but it is not known exactly how these numbers are distributed. In this paper we prove that integers from the segment [−n, n] lie in the spectrum of Tn for any n ≥ 31. Using this fact we also prove the main result of this paper that a segment of quadratic length with respect to n lies in the spectrum of Tn.

AB - A Transposition graph Tn is defined as a Cayley graph over the symmetric group Symn generated by all transpositions. It is known that the spectrum of Tn consists of integers, but it is not known exactly how these numbers are distributed. In this paper we prove that integers from the segment [−n, n] lie in the spectrum of Tn for any n ≥ 31. Using this fact we also prove the main result of this paper that a segment of quadratic length with respect to n lies in the spectrum of Tn.

KW - Transposition graph

KW - integral graph

KW - spectrum

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85212338449&origin=inward&txGid=f7b8aadd0bd756f5cffdbac8697d4c9f

UR - https://www.mendeley.com/catalogue/dd2a8f59-57e5-3bed-8357-526ea02fde92/

U2 - 10.33048/semi.2024.21.061

DO - 10.33048/semi.2024.21.061

M3 - Article

VL - 21

SP - 927

EP - 939

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 2

ER -