Message #1622

From: djs314djs314 <djs314djs314@yahoo.com>
Subject: Hi everyone, I’m back!
Date: Fri, 29 Apr 2011 22:47:11 -0000

Hello my friends,

First of all, I very deeply apologize for my inexplicable behavior when I suddenly and mysteriously left this group of very close friends over half a year ago. I have had some very serious issues going on in my life. In November I was hospitalized for a couple of weeks. To be a bit further ambiguous (sorry!), my departure was related to a symptom of my multiple illnesses. Of course, I can’t blame a foolish, consciousness decision entirely on a symptom, and don’t intend to. If any of you really want to know the whole story, I’ll share it, but with some hesitation! :) Melinda, you probably deserve an explanation, so I will send one to you privately at your request. Again, I apologize for my behavior, but am very much looking forward to being an active member again, if you will have me.

A very meaningful conversation with my good friend Roice inspired me to rejoin this group. I have wanted to for a while, but was honestly afraid of how everyone would respond. Roice helped me realize that I am among friends, and don’t need to worry about such things.

Well, I’m honestly thrilled to be back! :D I have so much to catch up on! I’ve only briefly scanned some of the recent messages, but I see that Magic120Cell and Klein’s Quartic have some new solvers! And of course, there have been contests (blindfold solving?!) and new programs. I’ll have to check out all that!

Hopefully my reintroduction will inspire me to help out and contribute wherever I can. I would like to get back into the combinatorics of the puzzles. Specifically, I’ve been promising myself for quite a while to find the order of the ‘n^d super-superhypercube group’ (at least that is what I call it! :) ). A super-supercube is like a Rubik’s Cube of any size in which every cubie is either on the surface or on the inside of the cube; the cube is solid. Any layer can be twisted. Also, each cubie has a unique identity and orientation (imagine that each face of each cubie has a unique integer associated to it). Obviously I don’t need to expalin how this extends to higher dimensions. My goal is to find a formula for the number of visually ditinguishable permutations of a cube of arbitrary size, >= 2, and arbitrary dimension, >= 3, that can be produced by a sequence of legal moves from the solved position

Also, there are so many other areas I could investigate. If Andrey would like, I can supply an explicit 7-dimensional formula for counting cube permutations, but that probably isn’t necessary. (My general formula handles all dimensions, and who needs such a formula anyway? ;) ) There is also Klein’s Quartic (if you guys haven’t figured it out already), general MagicTile puzzles, general MagicCube4D 2.0 puzzles, etc. I know such efforts are not terribly important to the group, but they do provide me some satisfaction and I would be happy to provide any new formulas I find.

My page of research has moved again, by the way, it is now here:

http://seti.weebly.com/channel.html

Amongst the materials are formulas for n^4, n^5, n^6, and n^d permutations, my Magic120Cell paper, my paper deriving the n^4 formula, and a coloring result for Magic120Cell.

I would also like to wish a warm welcome to any members who may have joined since my unfortunate departure. I wish you the best, and look forward to meeting you!

And Melinda, I had previously promised to help you with some research for MagicCube4D 2.0. If you still require my assistance, I am ready to help as soon as possible.

Thank you everyone so much for your understanding and patience. :) It’s time for me to browse the messages and download some programs! I’ll be writing again soon, and have a great day!

All the best,
David