mersenneforum.org  

Go Back   mersenneforum.org > Fun Stuff > Puzzles

Reply
 
Thread Tools
Old 2020-09-12, 03:25   #23
0scar
 
Jan 2020

22×3 Posts
Default

Quote:
Originally Posted by SmartMersenne View Post
Yes, the identity mapping is counted as a permutation.

And the mapping can have two disconnected cycles, but I doubt that it would yield a solution.

Here is how you should define the mapping: [1,2,0,4,3] where the indices are the original numbers and the entries are the result of the permutation.
I didn't know the chosen "cycle notation" too, I always used the "one-line notation" described by SmartMersenne.
Wikipedia has an useful paragraph about them (https://en.wikipedia.org/wiki/Permutation#Notations).
If we want to arrange the numbers from 0 to 6 in descending order, we have:
the one-line notation [6,5,4,3,2,1,0],
the cycle notation (0,6)(1,5)(2,4)(3),
but 1-cycles like (3) are often omitted.

For all RPS(n) games with n<=5, non-trivial automorphisms have exactly one cycle (more precisely, one n-cycle), but this property doesn't hold in general.
I guess it isn't spoiling to show the following RPS(7) game, far from being optimal:

0 -> 1, 2, 3
1 -> 4, 5, 6
2 -> 1, 4, 5
3 -> 1, 2, 6
4 -> 0, 3, 6
5 -> 0, 3, 4
6 -> 0, 2, 5

It admits two non-trivial automorphisms:
[2,4,5,1,3,0,6], or (0,2,5)(1,4,3)(6)
[5,3,0,4,1,2,6], or (0,5,2)(1,3,4)(6)
0scar is offline   Reply With Quote
Old 2020-09-24, 09:43   #24
SmartMersenne
 
Sep 2017

7610 Posts
Default

Is it only me or are you also annoyed with less frequent updates and feedback from the new puzzlemaster? I mean the previous guy was also slow but not that much.

Only on two occasions the previous puzzlemaster updated the website once a month but that was due to technical difficulties on the website and he kept the email communication going. This guy doesn't even reply to emails or misses correct answers.

I don't think they care as much as we do, and I am starting to question why I care at all.
SmartMersenne is online now   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
September 2019 Xyzzy Puzzles 10 2019-10-08 13:47
September 2018 Xyzzy Puzzles 2 2018-10-11 15:31
September 2017 R. Gerbicz Puzzles 21 2018-03-17 13:19
September 2016 Batalov Puzzles 8 2016-10-04 14:10
Anyone going to Vienna in September? fivemack Factoring 1 2007-09-07 00:29

All times are UTC. The time now is 09:50.

Thu Sep 24 09:50:38 UTC 2020 up 14 days, 7:01, 0 users, load averages: 1.04, 1.33, 1.41

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.