New paper on the arXiv

[Vince Vatter]

The members of this group might be interested in a paper that Michael Engen and I just posted on the arXiv:

https://arxiv.org/abs/1810.08252

The paper concerns this and other notions of super-permutations. Of course, as luck would have it, we submitted the paper to the arXiv the afternoon before Greg Egan's breakthroughs, so the section on that version of the problem will have to be updated. Any comments on or criticisms of the paper would be appreciated.

Cheers,

Vince

[Robin Houston]

Very interesting! Thank you for sharing this with the group.

The only thing I noticed on a quick first skim is your Proposition 2.3, where you write “It is also remarkable that the lower bound established by Ashlock and Tillotson has never been improved.”

The lower bound has been improved, I believe, to n! + (n-1)! + (n-2)! + (n-3). Unfortunately the proof of this is hard to cite, since it appears on a wiki page credited to “Anonymous”, in the section “The Lower Bound” of http://mathsci.wikia.com/wiki/The_Haruhi_Problem. It was added on September 17, 2011 by user “Renaldo Moon”.

The proof is presented in a rather informal style, and it took a bit of work for me to convince myself that the measure N2 can be defined rigorously in a way that lets the proof go through as described. But I believe it can: I’ll post about that separately.

It’s exciting to see more people becoming interested in superpermutations.

Best wishes,

Robin

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