MMS-type problems for Johnson scheme
I.Yu.Mogilnykh, K.V.Vorob'ev, A.A.Valyuzhenich
TL;DR
This paper investigates minimization problems related to the number of nonzero or negative entries in vectors from the eigenspaces of the Johnson scheme, connecting to conjectures and support problems in algebraic combinatorics.
Contribution
It introduces new minimization problems for eigenspaces of the Johnson scheme and relates them to existing conjectures and support problems, extending prior work.
Findings
Formulated minimization problems for eigenspaces.
Connected problems to the Manikam-Miklós-Singhi conjecture.
Provided asymptotic insights into support problems.
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-Mikl\'{o}s-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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Finite Group Theory Research