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Title :A partial order on the symmetric groups defined by 3-cycles
Authors :Maeda, Takashi
Authors alternative :前田, 高士
Issue Date :30-Dec-2002
Abstract :We define a partial order on the symmetric group S_n of degree n by x ≥ y iff y = a_1 ··· a_kx with i(y) = i(x) + 2k where a_1, ··· , a_k are 3-cycles of increasing or decreasing consecutive three letters and i(*) is the number of inversions of the element * of S_n, on the analogy of the weak Bruhat order. Whether an even permutation is comparable to the identity or not in this ordering is considered. It is shown that all of the even permutations of degree n which map 1 to n or n - 1 are comparable to the identity.
Type Local :紀要論文
ISSN :1344-008X
Publisher :Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus
URI :http://hdl.handle.net/20.500.12000/16107
Citation :Ryukyu mathematical journal Vol.15 p.19 -42
Appears in Collections:Vol.15 (2002)

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