I have 2 generating functions, and I’m trying to show they’re equal algebraically. Anyone see a nice trick??

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I have 2 generating functions, and I’m trying to show they’re equal algebraically. Anyone see a nice trick??

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haha no. I’ve tried but I cant think of something slick. Did yours for the first part look something like

1/(1-x^i) – x^i?

sure but you can write them as (1-x^i+x^(2i))/(1-x^i) etc.

what about for the other one? I have

(1/1-x^2i)(1/1-x^(6i-3))

Kyla the numerator 1-x^i+x^(2i)= (1+x^3i)/(1+x^i). Try that

It is you Kyla, right? LoL if not I meant kyqu

yes! ha. for the second one, I also have a factor of 1/(1-x). still not seeing equality but maybe it’s right in front of me

doesnt that term mean you’re including 1’s in your partition?

nevermind about that!!

and the algebra magic finally happened. thanks! let’s talk face to face on some of the others??!

hahaha yey! yes let’s.