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

Daniel V. Mathews

doi:10.4171/JEMS/1180

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

Daniel V. Mathews

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

1 Citation (Scopus)

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 (Formula Presented), 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.

Original language	English
Pages (from-to)	4201-4205
Number of pages	5
Journal	Journal of the European Mathematical Society
Volume	24
Issue number	12
DOIs	https://doi.org/10.4171/JEMS/1180
Publication status	Published - 2022

Keywords

Clifford algebras
Sensitivity conjecture

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10.4171/JEMS/1180Licence: CC BY

Cite this

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title = "The sensitivity conjecture, induced subgraphs of cubes, and Clifford algebras",

abstract = "We give another version of Huang{\textquoteright}s proof that an induced subgraph of the n-dimensional cube graph containing over half the vertices has maximal degree at least (Formula Presented), 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.",

keywords = "Clifford algebras, Sensitivity conjecture",

author = "Mathews, {Daniel V.}",

note = "Funding Information: The author is supported by Australian Research Council grant DP160103085. Publisher Copyright: {\textcopyright} 2021 European Mathematical Society.",

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AB - 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 (Formula Presented), 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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The sensitivity conjecture, induced subgraphs of cubes, and Clifford algebras

Abstract

Keywords

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Quantum invariants and hyperbolic manifolds in three-dimensional topology

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

Abstract

Keywords

Access to Document

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Quantum invariants and hyperbolic manifolds in three-dimensional topology

Cite this