A Note on the Factorization of Permutations into Cycles

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

References

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