Efficient enumeration of all ladder lotteries and its application

Katsuhisa Yamanaka, Shin ichi Nakano, Yasuko Matsui, Ryuhei Uehara, Kento Nakada

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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 L1 and L2 of a permutation, there exists a sequence of local modifications which transforms L1 into L2. 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 languageEnglish
Pages (from-to)1714-1722
Number of pages9
JournalTheoretical Computer Science
Issue number16-18
Publication statusPublished - Mar 28 2010
Externally publishedYes


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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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