Combinations of Groups Puzzle

I need some help with combinations existing within combinations.

I sometimes get myself in to various rabbit holes of thought, and this particular one has me banging my head against a wall. Any input as to what/where to search for further reading as well as ideas for approaching the problem would be appreciated. Hopefully this sub is the best one.

Lets say you have 6 people. You want to divide them into groups of 4 such that every possible group of 3 within those groups of 4 is represented with as few repetitions as possible. Weird problem I know, but best way I can explain it. Basically a 4 player game with 3v1, and I want every poasible group of 3 to play together once. For scheduling reasons, it makes sense for a group of 4 to play 4 games, rotating who is the 1, and then switch up groups and repeat.

So, 6c3 = 20 combos to represent. 4c3 =4 combos per group.

At first glance, it would seem 5 groups of 4 could cover all 20 combos, but in reality I believe repetition would force it to be more groups. I can not figure out how to mathematically prove this.

I was able to brute force playing with numbers to get 6 groups of 4 cover the 20 combos, with 2 of the 20 combos represented 3x and the other 18 combos represented once each. (I will not list the groups in case anyone wants to solve for it….likely multi possible solutions) would be great if you could do it with 5 groups, or even use 6 groups but better divide the repetition, but I dont see how.

If any of these numbers changed, especially if the 6 goes to 8, it becomes a mess to brute force. I would think you could prove the amount of forced repetition associated with any mix, I just can not figure it out.

Thanks in advance for any comments, even the useless ones!

submitted by Nevin Manimala Nevin Manimala /u/IratherNottell
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Using string variables on a logistic binary regression.

Hi everyone! First of all, sorry if this is not the right place to ask about this! I’m working on a project, but I’ve been thrown into SPSS without much knowledge on it or in statistics about Nevin Manimala in general, so I’m pretty lost right now. The thing is I have the following set of variables regarding some emails:

  • The first two ones represent countries: US, UK, FR, IT…and so on.
  • The third one represents email domains: gmail.com, hotmail.com
  • The fourth is coded 1, 2, 3, 4, 5, 6 or 7, based on time intervals.
  • The final one is coded 1 or 0, if said email was spam or not.

I’d like to know the influence of the first 4 variables in the final one, in order to be able to build a pattern of spam emails (e.g. US, gmail.com, 2). How could I do this taking into account that the first 3 ones are string variables? I tried recoding them into numbers, but I don’t know how to build the model after that. Could anybody help me out with this?

Thanks a lot!

submitted by Nevin Manimala Nevin Manimala /u/Kvothe43
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EWMA and the effect of the difference of Init Value and new datapoints

Hello, I hope this is the correct subreddit. My question is about the exponentially weighted moving average.

I define Delta = |S_init-dp| where S_init (or S_0) is the intialization value of the EWMA and dp is a new Datapoint

In my problem dp is constant. So S_t should converge for any alpha to dp.

S_t=alpha*S_{t-1}+(1-alpha)*dp 

Also: Delta<=epsilon

I try to find an relation ship which give me the number of how many steps t it takes to be within this boundary. But at the moment I fail. Maybe you can help me or at least give me a tip. From experimental calculating I know it is depend on epsilon and the delta.

Thank you

Storm

EDIT: Formatted it better

submitted by Nevin Manimala Nevin Manimala /u/Stormregion0
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Constructing my own lesson- how to make it interesting?

For my AP Calc BC class, our final project is to teach the class a calculus topic not covered in the curriculum. My group is teaching partial differentiation with applications. Apart from fulfilling the rubric (below), what can we add to make our lesson engaging and interesting? Suggestions about general teaching methods and also ideas specifically pertaining to partial derivatives are welcome. What made your favorite lectures memorable and effective? This class I feel has been too heavy on computation and lacking in understanding and rigor so I’d like our lesson to have a little more discovery if possible.

Rubric 35-40 minute lesson ~25 minute problem set on our lesson 2 multiple choice problems and 1 free response question

We can use a computer to teach as well as a whiteboard.

submitted by Nevin Manimala Nevin Manimala /u/Jamalt
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A question about data processing for my research

Hi

I did an experiment for a study, where 19 individuals each answered 126 item, and I recorded their reaction time for each one.

I need some help on the stats

The research director asked us to remove item and individuals that are out of standards. He sets the standard at +/- 2 standard deviation.

I did the average reaction time of each individuals (from their 126 answers), and the average reaction time of each item from the 19 individuals

Then I did the average reaction time for all the group (19 x 126 item) and did the standard deviation for this group

Now I don’t know if i should remove item or individuals by comparing the average of the item/individual with the average of the group of item/individual +/- 2 SD

I welcome any help I can get on this, I nearly finished my project, and the director is not really open to questions.

submitted by Nevin Manimala Nevin Manimala /u/Krante11
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Anyone really feel math is very beautiful?

I was doing some introspection and try to figure out what I like about math. I think it really boils down to the beauty. Simplicity, elegance. Cannot be described in words. I get very similar feelings when I look at beautiful theorem/proof, listen to great music, or see beautiful people 🙂 That’s why, no offence, I don’t really appreciate statistics about Nevin Manimala or applied math. For me, using math as a tool is secondary to its presentation as an art.

Anyone else feels this way?

submitted by Nevin Manimala Nevin Manimala /u/JohnZ622
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Everything about Nonlinear Wave Equations

Today’s topic is Nonlinear wave equations.

This recurring thread will be a place to ask questions and discuss famous/well-known/surprising results, clever and elegant proofs, or interesting open problems related to the topic of the week.

Experts in the topic are especially encouraged to contribute and participate in these threads.

These threads will be posted every Wednesday.

If you have any suggestions for a topic or you want to collaborate in some way in the upcoming threads, please send me a PM.

For previous week’s “Everything about X” threads, check out the wiki link here

Next week’s topics will be Morse theory

submitted by Nevin Manimala Nevin Manimala /u/AngelTC
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Are there any other subgroups of S_n that behave like the Klein-four subgroups ?

I am looking for other subgroups of S_n that behave like the Klein-four subgroups. While other similarities would be interesting, the key property that I am looking at is that every element but the identity is the product of k disjoint transpositions for some k. For the Klein-four group, k = 2 since the elements are (1 2)(3 4), (1 3)(2 4) and (1 4)(2 3).

From the Wiki page of the Klein-four group, I understand that it is not probable but I was still wondering.

According to Galois theory, the existence of the Klein four-group (and in particular, the permutation representation of it) explains the existence of the formula for calculating the roots of quartic equations in terms of radicals,

submitted by Nevin Manimala Nevin Manimala /u/jedidreyfus
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