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The sensitivity conjecture, induced subgraphs of cubes, and Clifford algebras

Name: The sensitivity conjecture, induced subgraphs of cubes, and Clifford algebras
Creator: Daniel V. Mathews
Keywords: Rings and Algebras (math.RA), 05C50, 15A66, FOS: Mathematics, Mathematics - Combinatorics, Mathematics - Rings and Algebras, Combinatorics (math.CO), 0101 mathematics, 01 natural sciences

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 15 Nov 2021Embargo end date: 01 Jan 2019Publisher:European Mathematical Society - EMS - Publishing House GmbHJournal:Journal of the European Mathematical Society, volume 24, pages 4,201-4,205 (issn: 1435-9855, eissn: 1435-9863,

Authors: Daniel V. Mathews;

doi: 10.4171/jems/1180 , 10.48550/arxiv.1907.12357

arXiv: http://arxiv.org/abs/1907.12357

The sensitivity conjecture, induced subgraphs of cubes, and Clifford algebras

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Abstract

We give another version of Huang’s proof that an induced subgraph of the {n} -dimensional cube graph containing over half the vertices has maximal degree at least {\sqrt{n}} , which implies the Sensitivity Conjecture. This argument uses Clifford algebras of positive definite signature in a natural way. We also prove a weighted version of the result.

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Keywords

Rings and Algebras (math.RA), 05C50, 15A66, FOS: Mathematics, Mathematics - Combinatorics, Mathematics - Rings and Algebras, Combinatorics (math.CO)

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ARC| Discovery Projects - Grant ID: DP160103085