Yıl 2017, Cilt 22, Sayı 22, Sayfalar 125 - 132 2017-07-11
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## A Note on the Factorization of Permutations into Cycles

#### J. Elder [1] , O. Vega [2]

##### 156 121

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.

Permutation, product of cycles
• 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.
Konular Matematik ve İstatistik Makaleler Yazar: J. Elder Yazar: O. Vega
 Bibtex @araştırma makalesi { ieja325937, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2017}, volume = {22}, pages = {125 - 132}, doi = {10.24330/ieja.325937}, title = {A Note on the Factorization of Permutations into Cycles}, key = {cite}, author = {Vega, O. and Elder, J.} } APA Elder, J , Vega, O . (2017). A Note on the Factorization of Permutations into Cycles. International Electronic Journal of Algebra, 22 (22), 125-132. DOI: 10.24330/ieja.325937 MLA Elder, J , Vega, O . "A Note on the Factorization of Permutations into Cycles". International Electronic Journal of Algebra 22 (2017): 125-132 Chicago Elder, J , Vega, O . "A Note on the Factorization of Permutations into Cycles". International Electronic Journal of Algebra 22 (2017): 125-132 RIS TY - JOUR T1 - A Note on the Factorization of Permutations into Cycles AU - J. Elder , O. Vega Y1 - 2017 PY - 2017 N1 - doi: 10.24330/ieja.325937 DO - 10.24330/ieja.325937 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 125 EP - 132 VL - 22 IS - 22 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.325937 UR - http://dx.doi.org/10.24330/ieja.325937 Y2 - 2018 ER - EndNote %0 International Electronic Journal of Algebra A Note on the Factorization of Permutations into Cycles %A J. Elder , O. Vega %T A Note on the Factorization of Permutations into Cycles %D 2017 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 22 %N 22 %R doi: 10.24330/ieja.325937 %U 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 (Temmuz 2017): 125-132. http://dx.doi.org/10.24330/ieja.325937