Sorting and generating reduced words
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We introduce a partial order on the set of all reduced words of a given permutation ω, called directed-braid poset of ω. This poset enables us to produce two algorithms: One is a sorting algorithm applied to any reduced word of ω and aims to obtain the natural word (i.e. lexicographically largest reduced word); the other one is a generation algorithm applied to the natural word and returns the set of all reduced words of ω.
KeywordsPartial Order Generation Algorithm Coxeter Group Lexicographic Order Sort Algorithm
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- 2.A. Garsia, The saga of reduced factorizations of elements of the symmetric group, Publications du LaCIM, Université du Québec a Montréal, Canada, Vol. 29, 2002.Google Scholar
- 3.D. E. Knuth, The Art of Computer Programming, 3. Sorting and Searching (second ed.), Addison-Wesley, (1998).Google Scholar