A Note on the Factorization of Permutations into Cycles

Authors : J ELDER, O VEGA

Pages : 125-132

Doi:10.24330/ieja.325937

View : 8 | Download : 12

Publication Date : 2017-07-11

Article Type : Research Paper

Abstract :We find conditions on $k, n\in \N$, where $3\leq k\leq n$ for which a permutation in $S_n$ can be written as a product of distinct $k$-cycles in $S_{n+i}\setminus S_n$, for some $i\in \N$. This result generalizes a problem that was solved in 2010 in an episode of the television show Futurama:  the so-called Futurama Theorem.
Keywords : Permutation, product of cycles