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Efficient Enumeration of All Ladder Lotteries with k Bars
Katsuhisa YAMANAKA Shin-ichi NAKANO
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2014/06/01
Online ISSN: 1745-1337
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
algorithm, enumeration, ladder lottery, family tree,
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A ladder lottery, known as the “Amidakuji” in Japan, is a network with n vertical lines and many horizontal lines each of which connects two consecutive vertical lines. Each ladder lottery corresponds to a permutation. Ladder lotteries are frequently used as natural models in many areas. Given a permutation π, an algorithm to enumerate all ladder lotteries of π with the minimum number of horizontal lines is known. In this paper, given a permutation π and an integer k, we design an algorithm to enumerate all ladder lotteries of π with exactly k horizontal lines.