I managed to improve the techniques of a year-old paper to get a significantly stronger result. I used original ideas, but a large part relies upon results of the original paper. (to the point that half the paper may be recapping the lemmas of the past paper)

Q1) Is it acceptable to ask the author of the original paper if they would like to collaborate?

I have heard that Paul Erdos would do this, which is something I highly admire. However, I am an undergraduate, so I fear my invitations would not be appreciated.

Q2) If it is acceptable, how do I make sure to make my invitation not pushy or expectant?

I'm thinking of writing something like:

I was wondering if anyone else had already achieved this result, and if it would be fit for publishing. If yes, while I fear it maybe rude to invite you to collaborate, please let me know if you are at all interested in getting involved.

I managed to improve the techniques of a year-old paper to get a significantly stronger result. I used original ideas, but a large part relies upon results of the original paper. (to the point that half the paper may be recapping the lemmas of the past paper)

Q1) Is it acceptable to ask the author of the original paper if they would like to collaborate?

I have heard that Paul Erdos would do this, which is something I highly admire. However, I am an undergraduate, so I fear my invitations would not be appreciated.

Q2) If it is acceptable, how do I make sure to make my invitation not pushy or expectant?

I'm thinking of writing something like:

I was wondering if anyone else had already achieved this result, and if it would be fit for publishing. If yes, while I fear it may be rude to invite you to collaborate, please let me know if you are at all interested in getting involved.