On the cardinality of a factor set in the symmetric group
2014 ◽
Vol 07
(02)
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pp. 1450027
Keyword(s):
Let n be a positive integer, σ be an element of the symmetric group [Formula: see text] and let σ be a cycle of length n. The elements [Formula: see text] are σ-equivalent, if there are natural numbers k and l, such that σk α = βσl, which is the same as the condition to exist natural numbers k1 and l1, such that α = σk1 βσl1. In this work, we examine some properties of the so-defined equivalence relation. We build a finite oriented graph Γn with the help of which is described an algorithm for solving the combinatorial problem for finding the number of equivalence classes according to this relation.
2012 ◽
Vol 26
(25)
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pp. 1246006
2008 ◽
Vol 78
(3)
◽
pp. 431-436
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Keyword(s):
1989 ◽
Vol 41
(5)
◽
pp. 830-854
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1958 ◽
Vol 13
◽
pp. 135-156
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Keyword(s):
2016 ◽
Vol 25
(14)
◽
pp. 1650076
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Keyword(s):