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Corpus ID: 53656920

MMS-type problems for Johnson scheme

@article{IYuMogilnykh2018MMStypePF,
title={MMS-type problems for Johnson scheme},
author={I.Yu.Mogilnykh and K.V.Vorob'ev and A.A.Valyuzhenich},
journal={arXiv: Combinatorics},
year={2018}
}

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-Miklos-Singhi conjecture proven by Blinovski and the minimum support problem for the eigenspaces of the Johnson graph, asymptotically solved by authors in a recent paper.

We study a class of highly regular t-designs. These are the subsets of vertices of the Johnson graph which are completely regular in the sense of Delsarte [2]. In [9], Meyerowitz classified the… Expand

In this article the parameter matrices are enumerated of all perfect 2-colorings of the Johnson graphs J(8, 3) and J(8, 4), and several constructions are presented for perfect 2-coloring of J(2w, w)… Expand

We study the perfect 2‐colorings (also known as the equitable partitions into two parts or the completely regular codes with covering radius 1) of the Johnson graphs J(v,3) . In particular, we… Expand