- International Electronic Journal of Algebra
- Vol: 22 Issue: 22
- A Note on the Factorization of Permutations into Cycles
A Note on the Factorization of Permutations into Cycles
Authors : J. Elder, O. Vega
Pages : 125-132
Doi:10.24330/ieja.325937
View : 12 | Download : 12
Publication Date : 2017-07-11
Article Type : Research
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