### Abstract

A ladder lottery, known as "Amidakuji" in Japan, is a common way to choose a permutation randomly. A ladder lottery L corresponding to a given permutation π is optimal if L has the minimum number of horizontal lines among the ladder lotteries corresponding to π. In this paper we show that for any two optimal ladder lotteries L_{1} and L_{2} of a permutation, there exists a sequence of local modifications which transforms L_{1} into L_{2}. We also give an algorithm to enumerate all optimal ladder lotteries of a given permutation. By setting π = (n, n - 1, ..., 1), the algorithm enumerates all arrangements of n pseudolines efficiently. By implementing the algorithm we compute the number of arrangements of n pseudolines for each n ≤ 11.

Original language | English |
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Pages (from-to) | 1714-1722 |

Number of pages | 9 |

Journal | Theoretical Computer Science |

Volume | 411 |

Issue number | 16-18 |

DOIs | |

Publication status | Published - Mar 28 2010 |

Externally published | Yes |

### Keywords

- Enumeration algorithm
- Family tree
- Ladder lottery
- Pseudoline arrangement

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Theoretical Computer Science*,

*411*(16-18), 1714-1722. https://doi.org/10.1016/j.tcs.2010.01.002