this is better

much better! :-)

okay, so would you like to fix a few things with the paper first?

We're talking about Ed01Prop 05?

the proof of prop 1

a^{c\diamond}

the convolution should be k-c not c, do you agree?

on the right after the and

Ah, I see. You're right, of course. I'll fix it.

Anything else?

also, on page 4, the statement about showing the proof should be omitted because we are publishing the proof in another paper correct?

rrrrrrright!

those were the only corrections i can see when reviewing the paper

great! I want to check the proof of prop 1 and send you an update. Edition 01 Proposal 06

Could you already talk with your profs? Did you make some other investigations?

none of them have responded as of now

but i have looked into journals a bit, but i was unable to make a decision on which journal would be appropriate

have you looked into it any

Ok, so we have to be patient.

What are your interests?

would this be considered combinatorics? the paper i mean

mathmatics haha, ive been looking into generating functions alot lately, my interest was sparked when i observed your proof

I think the best is to ask one of the profs from combinatorics. They should have the most experience in publishing such articles.

ah, i have not been in contact with any professors lately to be honest, perhaps i should contact someone new, do you think this is a good idea?

Btw: Don't be disappointed, if they refuse the paper. From my point of view it should have some more substance. Presumably, they will suggest that we add the proof (a short version of it).

do you have a short version of the proof on hand?

also i have a bit of a question about generating functions involving the coefficient of operator, i will send you the link to my question

No, since this need about one, two days of work, I'll do it, if it seems appropriate. As far as there is no strong request for it, I prefer to do some other (more interesting) stuff. :-)

Questions are welcome

i have been trying to do some independent studying with generating functions with the aid of the book "Generatingfunctionology"

Great! Wilf's GF is a great source to delve into this material!

I had a short look at your last MSE question. Too complicated to provide an answer within this chat! :-) I will think about it...

okay!

did i do the cauchy product correct?

i was worried i did it wrong

wait a moment

first of all there is a problem with the index $k$. I'ts not plausible that $k$ is a power and an index of the sum

oh, why?

The index $k$ is a so-called bound variable, valid only within the range of summation. But before you introduced the sum, you already had $k$ in use in the leftmost term. The conclusion is, that this expression is definitely wrong. :-;

You should replace the index $k$ of the sum with e.g. $l$ and then you'll observe, that the Cauchy product can't be calculated this way.

if i use l, then wouldnt the same be true?

I don't think so. Let's read the chain of equations from right to left.

The rightmost expression is the product of two exponential generating functions.

Multiplying two exponential generating functions results in an inner sum with binomial coefficient. Ok, BUT

en.wikipedia.org/wiki/General_Leibniz_rule which is what i used when i took the mth derivative of the product

The coefficients of the generated functions have to be raised to a power $\nu$ resp. $m-\nu$ and you take derivatives instead!

You see?

so the summations should be raised to those powers?

Leibniz rule is quite ok.

So, the leftmost and the middle expressions are equal. But the middle and the rightmost expressions are not equal.

shall i evaluate it further? show the logic within the question, perhaps you can catch my mistake

I've the feeling, that you won't find a simple expression which could be replaced with the rightmost one.

But you are very talented and maybe you see another good way ...

At the time I don't see how to continue. But, this is not important.

I'm pretty sure, that there is a direct way to prove your identity without taking the detour via another complicated identity as I did.

i actually see my mistake

it is actually quite interesting

Great!

i get a double summation instead of what i got before, ill update the question

i think i corrected it

I have the feeling that one identity somehow uses the inclusion-exclusion principle, while the other identity does not. Without exactly knowing where IEP comes into play. Presumably via the Stirling numbers. Maybe it's good to go one step back, forget the main identity for a short while and you could study Stirling numbers and the IEP to gain some more insight from a different perspective.

i actually privately discovered stirlings numbers on my own haha, i was trying to find the n-th derivative of the falling factorial function and i even came up with my own way of expressing the stirling number

which i found out later on that this recurrence relation was already found

:-)

but yea, what do you mean IEP?

im sorry, not good with abbreviations

inclusion-Exclusion Principle

I'm missing $\binom{m}{\nu}$ in your MSE expression ...

can you show me what you mean in an answer?

i think i understand

:-)

but can you show me what you mean just to be sure

Ahh, wait!

First of all, be aware that you will get soon a warning from MSE due to the high modification rate of your question.

ah okay

So, it's better to go on more slowly. Change at home, check and check again. Then change the MSE question.

I was thinking about multiplying two exponential generating functions.

But you multiply two finite sums. This could be different.

yea i took that part out

that is different

So, it's definitely better, to first rework it privately, before publishing it.

yea

now it makes more sense that it didn't work haha

:-)

When do you really plan to start with your studies at university? This autumn?

yes i believe so

its going to be weird to study at a place where i can get the resources i need

What do you mean? Which kind of resources do you miss?

conversing with people like you who can answer my questions about subjects i enjoy

not being the guy everyone goes to for help

i would like to be the guy that knows very little compared to my peers, so that i can learn from others for once

math stack exchange has provided that for now, but its not really in real time so it is a gradual learning process

my resources i mean other people with knowledge mostly

I see! But for sure you will meet a lot of interesting guys at university.

So, you need to be patient only for a short time!

yea, i was awarded a scholarship for $1500 at the university for my work on this paper, which is very nice

Hey, come on! This is fantastic! Why didn't you tell it before?

im not sure haha, it is pretty recent

So, you're joking! :-)

no im not, i recieved an email about it

Congrats!!!! :-)

i am going to go to an award ceremony

thanks :)

now, about publishing this paper, have you looked into any journals?

No!

Since you are the main author, it's your part and pleasure(!) to do these things.

ah I see, i have found a professor to email, have you made the corrections to the paper?

Also should i send our paper to this new professor? Would that be something i should hesitate to do?

I will do it this evening and send you the new proposal 06. But first I want to check it again.

okay

should i send him my current copy?

I think it's better to have first a personal visit.

He lives about 10 hours away from where i currently reside

You are in a much better position if you talk at first with the professors.

Ah, I see.

In this situation I would first send an email to him .

This email could be used to introduce yourself.

And in this email you could ask him if you could send him a paper for revision.

Dependent on his reaction the next steps will follow.

This is more appropriate than directly attack him with a paper, without giving him a chance to bear reference for you and your paper.

okay ill send the email now

You could also tell him about your presence in MSE and about your conversations with me.

Sorry, but in a few minutes I have to end our conversation. I will send you an update soon.

Btw: Do you know Hiroshi Yuki?

i do not, who is that?

He has written some very nice (and easy to read) books. Search for "Math Girls" in Amazon. Maybe you will love these books.

okay will do!

Does she have any generating function books?

yes and no

well ill let you get back to updating the paper, it was nice talking to you :) we should do this again another time

It's by far not that deep level you typically read. But I love the enthusiasm and the great presentation of some great ideas in mathe. It's a perfect starter for studying mathe.

Ok! It was nice to talk to you! Bye!

okay will do! ill be sure to find a copy

goodbye