Math Is Fun Forum

DeeK

Guest

Using the calculator for symmetrical permutations?

Dear team, first of all: great site!!!

I was wondering if it is possible to use your "Combinations and Permutations Calculator" to find all possible permutations of something like this:

list = 1,2,3,4,5 (actually you can omit the "3", i just wrote it in order to be more clear what i mean)

it is possible to combine only 1 with 5, and 2 with 4, symmetrically swapped with 3 as the center

the outcome should be:

1,2,4,5
1,4,2,5
2,1,5,4
2,5,1,4
5,2,4,1
5,4,2,1
4,1,5,2
4,5,1,2

If not, any idea how to program this in javascript?

Best regards,
Dee

ElainaVW

Member

Registered: 2013-04-29

Posts: 580

Re: Using the calculator for symmetrical permutations?

Hello,

Do you have a specific problem?

DeeK

Member

Registered: 2015-01-21

Posts: 2

Re: Using the calculator for symmetrical permutations?

Hi, not a specific problem, it is actually exactly as explained in my initial posting.

Is there a known way, either with the calculator (using patterns?), or programmatically (JS) to calculate all symmetrical combinations of 2 pairs as described?

Is there a known terminus for this kind of symmetrical combination i am talking about, so that i could continue my search online, if no success / answer found here?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Using the calculator for symmetrical permutations?

Hi;

Almost anything can be done with programming, for a full math solution I would need a little more explanation.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,974

Website

Re: Using the calculator for symmetrical permutations?

I hate full math solutions.

---

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Using the calculator for symmetrical permutations?

I do too, mostly they are unfathomable but I finished one a couple of days ago.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

DeeK

Member

Registered: 2015-01-21

Posts: 2

Re: Using the calculator for symmetrical permutations?

i try to repeat my explanation from my first post and being more clear.

list = 1,2,3,4,5

it is possible to combine only 1 with 5, and 2 with 4, symmetrically swapped with 3 as the center

the outcome should be:

1,2,3,4,5
1,4,3,2,5
2,1,3,5,4
2,5,3,1,4
5,2,3,4,1
5,4,3,2,1
4,1,3,5,2
4,5,3,1,2

(3 can also being left out, as it is the center and is not being picked / taken into account for the combinations)

trying to show you the relations by marking the numbers who are swapped together with either () or []:

(1),[2],3,[4],(5)
(1),[4],3,[2],(5)
[2],(1),3,(5),[4]
[2],(5),3,(1),[4]
(5),[2],3,[4],(1)
(5),[4],3,[2],(1)
[4],(1),3,(5),[2]
[4],(5),3,(1),[2]

or, to say it in different words, those 24 solutions / combinations of 1,2,4,5 (order important, repetition not allowed) are NOT VALID because 1,5 and 2,4 not symmetrical as a pair in relation to 3 (as explained above):

1,2,3,5,4
1,4,3,5,2
1,5,3,2,4
1,5,3,4,2
2,1,3,4,5
2,5,3,4,1
2,4,3,1,5
2,4,3,5,1
5,2,3,1,4
5,4,3,1,2
5,1,3,2,4
5,1,3,4,2
4,1,3,2,5
4,5,3,2,1
4,2,3,1,5
4,2,3,5,1