I. Yu. Mogilnykh, K. V. Vorob'ev, A. A. Valyuzhenich, “MMS-type problems for Johnson scheme”, Sib. Èlektron. Mat. Izv., 2018, Volume 15,Pages <nobr>1663

Discrete mathematics and mathematical cybernetics

MMS-type problems for Johnson scheme

I. Yu. Mogilnykh^ab, K. V. Vorob'ev^ab, A. A. Valyuzhenich^ab

^a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
^b Novosibirsk State University, st. Pirogova, 2, 630090, Novosibirsk, Russia

Abstract: In the current work we consider the minimization problems for the number of nonzero or negative values of vectors from the first and second eigenspaces of the Johnson scheme respectively. The topic is a meeting point for generalizations of the Manikam-Miklós-Singhi conjecture and the minimum support problem for the eigenspaces of the Johnson graph, asymptotically solved in [16].

Keywords: eigenspace, equitable partition, MMS-conjecture, Johnson scheme, Eberlein polynomials.

UDC: 519.1

MSC: 05E30

Received October 10, 2018, published December 17, 2018

Language: English

DOI: 10.33048/semi.2018.15.137