In my post of June 24
I requested some help on a sum (among other things).
In particular, we had a summation result that we were using in a paper
and we wanted to know if it was new or not.
We got three comments relevant to it
Method of differences due to Pascal
discrete calculus analog of the fact that the nth degree
Taylor expansion of a polynomial is the polynomials.
The first lemma is a direct consequence of the method of finite
differences; it says that the nth forward difference of a
polynomial of degree n-1 is identically zero.
The inner summation in the second identity is basically
computing the coefficients of the Newton Form
of the polynomial, although you seem to be using
a slightly different basis. Nevertheless, these
results are quite standard.
This raises a request and some question.
Authors of those comments (and others who know stuff)---
please email me more exact
references. I found some things on Google but it
would be good to know what to read and what is a good
source to reference. Preferable online.
In a paper if you are using a result that is known
how much detail should you put in?
Clearly put in that it is known and provide a references.
I would not want to frustrate my readers with
This is easily derived from the method of differences.
without providing a reference.
In this day and age an online reference if you can mange it.
If the result is not quite written down anywhere but your readers
could easily derive it using known techniques, then you do not
need to supply a proof. But this is not as clear a statement
as it sounds- it depends on how you define
readers, easily, known, and technique.
If the result is known but you have a cute proof of it
which seems new (hard to tell) then what do you do?
If the proof is short then I am more inclined to include it.
If its an e-journal than length matters less.
(This topic has been raised in a different form before---if Conferences proceedings
are CD's then why have a page limit?)
If there are no online references then I am more inclined to include a proof.
My only real point here is that its a QUESTION- what is
the cutoff for what is worth including?
There is no one answer.
Posted By GASARCH to Computational Complexity at 6/29/2009 11:25:00 AM