2
$\begingroup$

I've read about some studies on the Paley I Construction. Among them I found the following notations ( See this page: https://documents.uow.edu.au/~jennie/matrices/32P02.html ).

$$SNF:1,2^a,4^{b},8^{b},16^a,32$$

I am not familiar with these notations. Could you please recommend me some books or articles about it? Thanks in advance!

$\endgroup$
4
  • 2
    $\begingroup$ Smith Normal Form, my first guess, as in the answer. $\endgroup$
    – Will Jagy
    Apr 21 at 14:15
  • 1
    $\begingroup$ If you want the very basics about some topic in math, Wikipedia is always a good place to check: en.wikipedia.org/wiki/Smith_normal_form $\endgroup$ Apr 21 at 15:36
  • 1
    $\begingroup$ To complete the guess of @Will Jagy, in your example the SNF is given by the diagonal matrix $\operatorname{diag}(1,2^a,4^b,8^b,16^a,32,0,\ldots)$ for adequate non-negative integers $a,b$, where for each diagonal entry $d_i$ divides $d_{i+1}$. You can find additional details on the same page where you found the example: documents.uow.edu.au/~jennie/WEBPDF/1996_08.pdf $\endgroup$
    – F Zaldivar
    Apr 21 at 17:18
  • 1
    $\begingroup$ Brouwer and Haemers' "Spectra of Graphs" has a chapter about p-ranks, it is Chapter 13. In the last section of that chapter they discuss SNFs. Not the most basic reference but I think more in line with the type of SNF you are interested in, as a graph invariant. win.tue.nl/~aeb/2WF05/spectra.pdf By the way, the exponents a, b in your example are meant to indicate the multiplicity of the entry. So "2" occurs a times. $\endgroup$
    – Josh
    Apr 22 at 19:24

1 Answer 1

2
$\begingroup$

I think Richard Stanley's survey would be a good start. The published version is here.

Richard also has some slides regarding SNF.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.