Mapping Combinatorics 

Do you want it...? You have to say if you want it first haha 😎

​@@dibeos... I do, is me enough? :(

@@zackbuildit88 yessssss hahah we will make it! Actually, Sofia and I are studying a book about it and we have some very cool video ideas coming soon (around 2 weeks from now) 😎

@@dibeos HOORAY! I've been struggling to find any approachable resources for learning it honestly

@@zackbuildit88 we are happy to know that! 😎

That's awesome. There are very interesting math results related to permutations 😎

Thanks for your feedback! Well look, this was based on a book on combinatorics which was broken into three parts, all of which we touched on here, and their most essential concepts and branches. I think that fulfills the criterion of what it means to “map” a subject. Now, delving into each branch of combinatorics deeper into more advanced and particular subjects within each respective branch (enumeration, graph theory, an design theory) would be something we’d like to do in the near future 😎

@@tinyleopard6741 thanks! We are currently working on future videos where we will gradually dove deeper into combinatorics. Please tell us what you’d like to see in these future videos 😎

@@victork8708 that’s great! We will do it!!! 😎 stay tuned

@@palindrame awesome!! We will start working on it. But we already have very good ideas about how to make a video containing “everything” about Graph Theory 😎

@@dibeos love that! 🥂

@@palindrame we will post it in about 2 weeks. But do tell us, do you study graph theory? What are the math areas that interest you the most?

@@dibeos I am a student of Theoretical Computer Science; so anything remotely related to discrete mathematics really gets me excited. Having said that I don’t mind delving into rigorous pure math every now and then 😉.

@@palindrame that’s cool! now that you mentioned your background we understand your interests better. our goal is to create a huge library of videos on a great variety of fields of math and physics in the years to come 😎 have a nice day!

awesome! we will have more of it in the channel 😎

@@geoffreyfaust3443 yes, I do want to know how to improve my pronunciation. Thanks for the tip 😎 please keep on telling me how to pronounce words correctly in future videos. It really helps me to improve my English in the long run

@@dibeos OK, so FYI, the words INDEX and INDICES which are widely used to notate an array of numbers in math and physics, is pronounced in English in a cognate way to VERTEX and VERTICES (MATRIX and MATRICES pretty much follow the same pattern). English is a strange language.

@@diarmuidkeane1 As far as I know partitions are considered a part of both combinatorics and number theory. They study how numbers can be broken down into sums of other numbers, connecting to both fields. Your Python method sounds interesting and useful for exploring this concept! Can you tell me more about it? 😎

@@dibeos hey thanks for the reply - here is the script - Theres a lot to say about it - I've tried to document the methods to give some indication of the approach -- the motivation is to find a closed form expression for the partion count - from what I can see it appears to be possible but idont know yet and I have deliberately not looked it up on the intenet so pls no spoilers! ;) - -I hope to tidy it up push it to a gitlab repo at some point pls reach out if you have any questions - enjoy! from itertools import chain NUMBER = 14 def list_all_sums_of_pairs(number: int) -> list[list[int]]: """returns a list of all possible unique pairs of numbers whose sum equals the given number.""" return [[x, number - x] for x in range(1, number // 2 + 1)] def make_partition(partition: list[int]) -> list[list[int]]: """creates the list of partitions of degree n+1 from the given partition of degree n.""" def replace_last(splayed_pair: list[int]) -> list[int]: """A closure that returns the given partition in outer scope but with the final element replaces by the pair generated from splaying the original partition.""" return partition[:-1] + splayed_pair return list(filter(increasing, map(replace_last, list_all_sums_of_pairs(partition[-1])))) def increasing(nums: list[int]) -> bool: """predicate returns true if nums are non-strictly increasing in sequence.""" if len(nums) list[list[int]]: return list(chain(*list(map(make_partition, partition_list)))) def main(): result = layer = [[NUMBER]] while layer := make_partition_list(layer): result += layer print(result) print(len(result)) if __name__ == "__main__": main()

@@ifrazali3052 thanks!!! 😎

@@Cooososoo it sounds promising! Can you give more details?

@@dibeos Like generating functions

@@irvinep hi!! We will definitely as you say. About Riemann Steljis integral, I looked it up but did not understand it. I admit I need to think more about it, have a good grasp on it, and then look for a geometrical interpretation. But I will do it. It is in my to do list 😎

@@dibeos Thanks mate. I will wait.

@@goat2265 thank you!!! Every time someone comments something like that we feel super encouraged to increase the quality and quantity of videos on the channel. Stay tuned cause this is just the beginning 😎

@@Mahi2-k7i great idea!!! I will definitely post a video about it. And I agree with you about few videos about physics. I’m currently working on 2 physics videos to compensate for that. The goal of the channel is to have videos on math and mathematical physics. Please keep giving us good ideas like that!! 😎

@@dibeos 👍👍👍

Thank you so much!!!!!!!!!!! 😎 Tell us what kind of content you want and we will make it 😉

Both are great. Instead of competition let's have coalition so that we have lot of combinations and permutations ❤😂

@@mohankumaro2409 clever joke hahaha 😎

awesome, share your paper here with us!

​​@@dibeosdo you have any facebook id.

@@moonwatcher2001 thanks!!! Let us know what kind of content you’d like to see in the channel 😎 have a nice day

@@dibeos I love mapping of concepts and knowledge. Yours is awesome. Any mapping would be interesting

@@moonwatcher2001 great! We will create a playlist of “mappings” 😎

@@dibeos great!!!

@@SobTim-eu3xu yes!!! I hope you like it 😎

@@dibeos ofc, how I can't like it)

@@Satisfiyingvideo-uu9pw check my email on the description of the channel 😎

​@@dibeos 🤠

@@primenumberbuster404 😎