## Abstract

For a function f : {0, 1}^{n} → R and an invertible linear transformation L ∈ G L_{n} (2), we consider the function L f : {0, 1}^{n} → R defined by L f (x) = f (L x). We raise two conjectures: First, we conjecture that if f is Boolean and monotone then I (L f) ≥ I (f), where I (f) is the total influence of f. Second, we conjecture that if both f and L (f) are monotone, then f = L (f) (up to a permutation of the coordinates). We prove the second conjecture in the case where L is upper triangular.

Original language | English |
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Pages (from-to) | 4210-4214 |

Number of pages | 5 |

Journal | Discrete Mathematics |

Volume | 309 |

Issue number | 12 |

DOIs | |

State | Published - 28 Jun 2009 |

Externally published | Yes |

### Bibliographical note

Funding Information:First author is supported by the Adams Fellowship Program of the Israeli Academy of Sciences and Humanities. Second author is supported by the Giora Yoel Yashinsky Memorial Scholarship.

### Funding

First author is supported by the Adams Fellowship Program of the Israeli Academy of Sciences and Humanities. Second author is supported by the Giora Yoel Yashinsky Memorial Scholarship.

Funders | Funder number |
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Giora Yoel Yashinsky Memorial Scholarship | |

Israeli Academy of Sciences and Humanities |

## Keywords

- Boolean functions
- Discrete Fourier analysis
- Fourier-Walsh expansion
- Influences