Generating Function Intro | Counting With Power Series

In this video we introduce generating functions; a very cool way to solve counting problems using power series!

The book generatingfunctionology is mentioned in the video. Here is the link:

#GeneratingSeries #GeneratingFunction #EnumerativeCombinatorics

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[moslemasultana]

I didn’t find generating functions more amazing before!

[SuperMtheory]

Please make a future video (or more) abut generating functions. This introduction was great.

[holyshit]

I have used ordinary and exponential generating functions to solve recursive relations so far
so your video helped me to solve one problem from math forum

[moslemasultana]

very useful for olympiads. Thank you brother

[routemath]

Very cool problem, Prof, thanks for sharing!

[vtvtify]

Solved before watching the video, you taugh me the concept in one of the older videos. Thank you! If you could do IMO problems that would be lovely

[mehdisi]

Nice video. It would be great if you could find a way to find the x^100 factor coefficient without referring to the software.

[DinHamburg]

Is it necessary to multiply out the 4 series to get to the x^100 term or is there some advanced algebra to go to the desired coefficient directly? I guess, the 'naive, straight forward way' can be quite expensive for larger systems

[techdecker]

Would there be any way to use this technique to solve similar questions without the use of external tools such as Wolfram Alpha? Another great video by the way!

[syedmdabid]

The coefficient shows the partion number of the power but we could find how could we break a number n into r partition for a big number. So any trick?

[luizantonioponce]

Prof. OMAR
I loved the explanation. Congratulations.
However, I think there was a slight slip at the beginning.
Instead of (a0-a3) it should be a3 - a0, a1-a4 should be a4 - a1, ..and so on. However, it ended up not getting in the way of his explanation. Excuse me if I'm mistaken. With best wishes Professor PONCE - BRAZIL.

[백-kj]

how would you expand (1- x^3)^-5? will the powers always be a multiple of 3 as well? How would we know this?

[thedoublehelix]

How to solve a simple counting problem: 1) Invent calculus.
Also I don't see how writing a program would be any different than using the power series method in this case. The easiest program I can think of right now involved time complexity O(n^3) and I don't know if programing way to expand rational functions into power series will be any better.

[saga_]

Great video sir🙌 but I would be very grateful to u if u could tell me how to find coefficient of x^100 without using Wolframalpha