Covering the permutohedron by affine hyperplanes

Covering the permutohedron by affine hyperplanes

An almost cover of a finite set in the affine space is a collection of hyperplanes that together cover all points of the set except one. Using the polynomial method, we determine the minimum size of an almost cover of the vertex set of the permutohedron and address a few related questions.

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Veröffentlicht in:Acta mathematica Hungarica 2024, Vol.174 (2), p.453-461
Hauptverfasser: Hegedüs, G., Károlyi, GY
Format: Artikel
Sprache:eng
Schlagworte:
Hyperplanes
Mathematics
Mathematics and Statistics
Polynomials
Vertex sets
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Beschreibung
Zusammenfassung:An almost cover of a finite set in the affine space is a collection of hyperplanes that together cover all points of the set except one. Using the polynomial method, we determine the minimum size of an almost cover of the vertex set of the permutohedron and address a few related questions.
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-024-01462-7