### Abstract

How much can a permutation be simplified by means of cyclic rotations? For functions f:S_{n} → Z which give a measure of complexity to permutations we are interested in finding F(n) = max min f(σ), where the max is over σ ε{lunate} S_{n} and the min is over π which are cyclically equivalent to σ. The measures of complexity considered are the number of inversions and the diameter of the permutation. The effect of allowing a reflection as well as rotations is also considered.

Original language | English |
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Pages (from-to) | 1-11 |

Number of pages | 11 |

Journal | Discrete Mathematics |

Volume | 64 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1987 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*64*(1), 1-11. https://doi.org/10.1016/0012-365X(87)90235-4

**Extremal problems on permutations under cyclic equivalence.** / Erdős, P.; Linial, N.; Moran, S.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 64, no. 1, pp. 1-11. https://doi.org/10.1016/0012-365X(87)90235-4

}

TY - JOUR

T1 - Extremal problems on permutations under cyclic equivalence

AU - Erdős, P.

AU - Linial, N.

AU - Moran, S.

PY - 1987

Y1 - 1987

N2 - How much can a permutation be simplified by means of cyclic rotations? For functions f:Sn → Z which give a measure of complexity to permutations we are interested in finding F(n) = max min f(σ), where the max is over σ ε{lunate} Sn and the min is over π which are cyclically equivalent to σ. The measures of complexity considered are the number of inversions and the diameter of the permutation. The effect of allowing a reflection as well as rotations is also considered.

AB - How much can a permutation be simplified by means of cyclic rotations? For functions f:Sn → Z which give a measure of complexity to permutations we are interested in finding F(n) = max min f(σ), where the max is over σ ε{lunate} Sn and the min is over π which are cyclically equivalent to σ. The measures of complexity considered are the number of inversions and the diameter of the permutation. The effect of allowing a reflection as well as rotations is also considered.

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UR - http://www.scopus.com/inward/citedby.url?scp=45949121643&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(87)90235-4

DO - 10.1016/0012-365X(87)90235-4

M3 - Article

VL - 64

SP - 1

EP - 11

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1

ER -