People

on reddit are excited about

this paper published in 2012.

This is what the author claimed about his work (on reddit). (You can read more in the abstract.)

Xiphias said:

Rubik's cube can be realized as a semi-direct product between its subgroup of orientation and its subgroup of permutations [...] It has been done before, but not using the functions for orientation that I introduced, and according to my mentor, was not done properly until now.

He apparently used this for his master's thesis.

[HR][/HR]Also, here are some other papers that I found in the past year (I've been curious to see what's out there in comparison to my paper/book) that I never got to posting here (which might be of interest for those who don't know about them already).

I'm not for or against any of these papers (I didn't read them. I just skimmed through them, to be honest). I just want to let some know what's out there.

Move-count means with cancellation and word selection problems in Rubik's cube solution approaches
by Joseph Miller for a Phd disseration in 2012.

Rubik’s Cube Extended: Derivation of Number of States for Cubes of Any Sizeand Values for up to Size 25x25x25
by Ken F. Fraser (Revised in 2014.)

An Evolutionary Approach for Solving theRubik’s Cube Incorporating Exact Methods
by Nail El-Sourani, Sascha Hauke, and Markus Borschbach (2010)

and their follow-up paper (also published in 2010)

Design and Comparison of two EvolutionaryApproaches for Solving the Rubik's Cube
Rubik's Solving Approach by Edge-Centric Matching In Artificial Intelligence
by Hareesh B. N, Sangappa Kuragod, Mahesh K. Kaluti (2015)

The Rubik'S Crypto-Cube: A Trans-Composite Cipher
by Daniel R. Van der Vieren (2010)

Rubik's for Cryptographers:

In Paper form|

In article form
by Christophe Petit and Jean-Jacques Quisquater (2011)

Search methods for general permutation problems (Bachelor's thesis)
by Arthur Toenz (2012)

Zero Knowledge with Rubik's Cubes and Non-Abelian Groups
by Emmanuel Volte, Jacques Patarin, and Valerie Nachef (2011 or later)

On Rubik's Cube
by Olof Bergvall, Elin Hynning, Mikael Hedberg, Joel Mickelin, and Patrick Masawe (2010)

Higher Mathematical Concepts Using the Rubik's Cube
by Pawel Nazarewicz (2002)

[HR][/HR]The following isn't a paper about the Rubik's cube, but by the author solving twisty puzzles, he got an idea on how to expand on an old number theory topic. (For more info, read

this paper, and watch

this video, describing the background of what got him started in writing the following paper which ultimately earned him a fields medal in 2014.)

Higher composition laws I: A new view on Gauss composition, and quadratic generalizations
by Manjul Bhargava (2001)

[HR][/HR]Here are some papers on commutator theory (but the Rubik's cube is not mentioned: these are just math papers on permutations)

On Commutators in Groups (This paper talks about the history of commutators as well.)

by Luise-Charlotte Kappe and Robert Fitzgerald Morse (2004 or later)

Odd permutations are nicer than even ones
By Robert Coria, Michel Marcusa, and Gilles Schaeﬀer (2014)

Even Permutations as Conjugates of Two Conjugate Cycles (This was the work cited in the "My Ultimate Commutator Challenge Thread")

By Edward Bertram (1969)

*I believe the following are derivative works of the above.*

Permutations as product of conjugate infinite cycles
By Edward Bertram (1971)

All even permutations with large support are commutators of generating pairs
by David Zmiaikou (2014)

A Property of Alternating Groups
by Henry Cejtin and Igor Rivin (2014)

[HR][/HR]Lastly, here's a paper on discussing constructing computer-assisted proofs. I thought since the proof that God's number is 20 (htm) and 26 (qtm) were proved in this manner, this might be interesting to some.

Future Prospects for Computer-Assisted Mathematics
by David H. Bailey and Jonathan M. Borwein (2005)