Lmst

#ThisWeeksFiddler, 20250411
This week the question is: Can You Grow a Hibiscus Hedge? #permutation #sequence Dean has three colors of the hibiscus: red, orange, and yellow. He wants to plant them in a straight hedge of shrubs (each of which is one color) so that the order appears somewhat random, but not truly random. More specifically, he […]

https://stuff.ommadawn.dk/2025/04/15/thisweeksfiddler-20250411/

Amikoj who like maths: I'm trying to find the name of a math operation. Please help if interested!

It's similar to "choose"
4 choose 2 = 6
because there are six ways to choose 2 things from four. Similarly,
5 choose 2 = 10
There are ten ways.

But what if the five things are in a circle and we don't (re)count as new instances the ones that look the same when rotated?
5 ___ 2 = 2 (I'm pretty sure)
The 2 items can be either 1 and 4 apart or 2 and 3 apart.
I'm looking for the underlined operation.

5 ___ 3 = 2
If the items are ABCDE, where E is connected to A, the two configurations are 1. ABC (three together), 2. ABD (two, skip one, one). In the case of 5 items ACD is equivalent to 2 because CDA is two, skip one, one.For my purposes they must be equivalent by rotation only, not by flipping.

6 ___ 3 = 4
ABCDEF has ABC, ABD, ABE, and ACE. All others should be equivalent if I counted correctly.

What is this operation called? 🙏

#maths #math #discretemath #permutation

#statstab #319 Small Sample Size Solutions [book]

Thoughts: This should just be the default text for psychologists, as most research fits the "small sample" label.

#smallsample #book #guide #bayesian #permutation #sem #metaanalysis #nof1 #missingdata

https://doi.org/10.4324/9780429273872

#statstab #318 Simple permutation tests in R
by #MacTheobio

Thoughts: A very good small sample problem solution is using permutation tests. But, there are various ways to conduct these.

#permutation #randomization #montecarlo #R #smallsample

https://mac-theobio.github.io/QMEE/lectures/permutation_examples.notes.html

One day, one decomposition
A215940: Difference between the n-th and the first (identity) permutation of (0,...,m-1), interpreted as a decimal number, divided by 9 (for any m for which 10! >= m! >= n)

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A215940.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A215940.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #difference #decimal #numbers #permutation #graph #threejs #webGL

Decomposition into weight × level + jump of A215940 in 2D (log(weight), log(level))

Decomposition into weight × level + jump of A215940 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

#statstab #303 When Your Permutation Test is Doomed to Fail

Thoughts: Permutation tests are great, except for when they're not. Skewed data + unbalanced samples.

#stats #permutation #ABtesting #ttest #power #skewed

https://doi.org/10.1080/00031305.2021.1902856

#statstab #257 Permutation tests are robust and powerful at 0.5% and 5% significance levels

Thoughts: Permutation tests are cool and useful to learn, although they come with some quirks.

#permutation #randomization #ttest #ordinal #metricdata

https://link.springer.com/article/10.3758/s13428-021-01595-5

Fun fact, the lowest #number that can be fully #divided by every natural number from 1 to 10 is 2520 while the #permutation of 10! is 3628800. Spent few hours to measure that graphically.

One day, one decomposition
A115921: Numbers k such that the decimal digits of phi(k) are a permutation of those of k

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A115921.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A115921.html

#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #decimal #numbers #digits #phi #permutation #graph #threejs #webGL

Decomposition into weight × level + jump of A115921 in 2D (log(weight), log(level))

Decomposition into weight × level + jump of A115921 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

🧬 Our new tool ARTEM identifies RNA 3D motifs based on their isostericity!

🚀 Check out kink-turn-like motifs with no kink, and crazy kink-turn variants in group II introns. 🔬

https://doi.org/10.1101/2024.05.31.596898

https://github.com/febos/ARTEM-KT
https://github.com/david-bogdan-r/ARTEM

#RNA #Science #Bioinformatics #StructuralBiology #Research #Innovation #Motif #3D #Structure #Kinkturn #kjunction #ARTEM #Permutation

#statstab #156 Exact and asymptotic p-values

Thoughts: An important stats lesson is to be specific with terms. Exact p-values are not the same as asymptotic p-values (what most tests report w/o specifying).

#pvalues #nhst #permutation #randomization

https://analyse-it.com/docs/user-guide/101/exact-asymptotic-p-values

One day, one decomposition
A085844: Numbers equal to a permutation (or rearrangement) of the digits of the sum of their proper divisors. Rearrangements which cause leading zeros are excluded

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A085844.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A085844.html

#decompwlj #maths #mathematics #OEIS #javascript #php #3D #numbers #permutation #digits #sum #proper #divisors #graph #threejs #webGL

Decomposition into weight × level + jump of A085844 in 2D (log(weight), log(level))

Decomposition into weight × level + jump of A085844 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Whiskeyleaks.now()

#emf #emf24 #emf2024 #emfcamp #emfcamp24 #emfcamp2024 #permutation

Durch Anime zur Mathematik: Wer beim Binge-Watching nicht allzu viel Zeit verschwenden möchte, sollte sich mit der Theorie der Superpermutationen beschäftigen.#Freistetter #FreistettersFormelwelt #Mathematik #Kombinatorik #Superpermutation #Permutation
Vier Millionen Jahre vor dem Fernseher

#statstab #48 Studentized permutation tests for non-i.i.d. hypotheses

Thoughts: Continuing my cleaning of RI approaches, this paper is a bit dense but shows a nice Welch's version of Rand tests.

#permutation #randomization #NHST #pvalues

https://www.sciencedirect.com/science/article/pii/S0167715297000436

#statstab #39 Permutation test for "sharp" vs "weak" null hyp

Thoughts: Perm/Rand tests have a different (often inappropriate) Null Hypothesis. The similarity in estimates to asymptomatic tests is misleading wrt their inference.

#permutation #nhst #statistics #statstodon #experiments

https://stats.stackexchange.com/questions/315891/permutation-tests-for-sharp-vs-weak-null-hypothesis

Friday Peevery Dept: That whole room full of #Monkeys with infinite time on their hands eventually reproducing the works of #Shakespeare thing ? Remember that ? Not even. It's not about the monkeys (though in reality that roomful of Monkeys is more likely to end with mostly blank pages, randomly dispersed typewriters and sh*t literally everywhere).#Probability and #Permutation are not enough. In fact it's much more likely we are living in a #Simulation...made by those very same monkeys.Your move