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A Note on the Factorization of Permutations into Cycles

Year 2017, , 125 - 132, 11.07.2017
https://doi.org/10.24330/ieja.325937

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.

References

  • R. Evans, L. Huang and T. Nguyen, Keeler's theorem and products of distinct transpositions, Amer. Math. Monthly, 121(2) (2014), 136-144.
  • R. Evans and L. Huang, Mind switches in Futurama and Stargate, Math. Mag., 87(4) (2014), 252-262.
  • H. Georgiev, The Futurama theorem explained, The Commutator, 2 (2010), 18-20.
  • T. Phillips, Math in the Media, Amer. Math. Soc., Original math on Futurama, (2010). http://www.ams.org/news/math-in-the-media/10-2010-media.
  • Previous Nominees & Winners of the Writers Guild Awards (last accessed on 08/15/16). http://awards.wga.org/wga-awards/previous-nominees-winners.
  • S. Singh, The Simpsons and their mathematical secrets, Bloomsbury, NY, 2013.
  • The prisoner of Benda, The Infosphere, the Futurama Wiki (last accessed on 08/15/16). http://theinfosphere.org/The_Prisoner_of_Benda.
Year 2017, , 125 - 132, 11.07.2017
https://doi.org/10.24330/ieja.325937

Abstract

References

  • R. Evans, L. Huang and T. Nguyen, Keeler's theorem and products of distinct transpositions, Amer. Math. Monthly, 121(2) (2014), 136-144.
  • R. Evans and L. Huang, Mind switches in Futurama and Stargate, Math. Mag., 87(4) (2014), 252-262.
  • H. Georgiev, The Futurama theorem explained, The Commutator, 2 (2010), 18-20.
  • T. Phillips, Math in the Media, Amer. Math. Soc., Original math on Futurama, (2010). http://www.ams.org/news/math-in-the-media/10-2010-media.
  • Previous Nominees & Winners of the Writers Guild Awards (last accessed on 08/15/16). http://awards.wga.org/wga-awards/previous-nominees-winners.
  • S. Singh, The Simpsons and their mathematical secrets, Bloomsbury, NY, 2013.
  • The prisoner of Benda, The Infosphere, the Futurama Wiki (last accessed on 08/15/16). http://theinfosphere.org/The_Prisoner_of_Benda.
There are 7 citations in total.

Details

Subjects Mathematical Sciences
Journal Section Articles
Authors

J. Elder This is me

O. Vega This is me

Publication Date July 11, 2017
Published in Issue Year 2017

Cite

APA Elder, J., & Vega, O. (2017). A Note on the Factorization of Permutations into Cycles. International Electronic Journal of Algebra, 22(22), 125-132. https://doi.org/10.24330/ieja.325937
AMA Elder J, Vega O. A Note on the Factorization of Permutations into Cycles. IEJA. July 2017;22(22):125-132. doi:10.24330/ieja.325937
Chicago Elder, J., and O. Vega. “A Note on the Factorization of Permutations into Cycles”. International Electronic Journal of Algebra 22, no. 22 (July 2017): 125-32. https://doi.org/10.24330/ieja.325937.
EndNote Elder J, Vega O (July 1, 2017) A Note on the Factorization of Permutations into Cycles. International Electronic Journal of Algebra 22 22 125–132.
IEEE J. Elder and O. Vega, “A Note on the Factorization of Permutations into Cycles”, IEJA, vol. 22, no. 22, pp. 125–132, 2017, doi: 10.24330/ieja.325937.
ISNAD Elder, J. - Vega, O. “A Note on the Factorization of Permutations into Cycles”. International Electronic Journal of Algebra 22/22 (July 2017), 125-132. https://doi.org/10.24330/ieja.325937.
JAMA Elder J, Vega O. A Note on the Factorization of Permutations into Cycles. IEJA. 2017;22:125–132.
MLA Elder, J. and O. Vega. “A Note on the Factorization of Permutations into Cycles”. International Electronic Journal of Algebra, vol. 22, no. 22, 2017, pp. 125-32, doi:10.24330/ieja.325937.
Vancouver Elder J, Vega O. A Note on the Factorization of Permutations into Cycles. IEJA. 2017;22(22):125-32.