Notes on writing papers

``The practice of listing abbreviations in lieu of correct bibliographic references is irresponsible,'' Krantz writes on page 76 of some book. If you want to help the reader as little as possible, imitate Krantz's hypothetical example of a minimalistic bibliography entry: ``Machedon, 1988.''

Readers may complain.
In response,
point out that the reader can easily find the cited work
given a tiny amount of information,
in this age of Google and CiteSeer and MathSciNet
and the Collection of Computer Science Bibliographies.
For example,
those of us with MathSciNet access
can do a search for `machedon and 1988`
and find details of two papers by Machedon in 1988;
presumably the reader of Krantz's hypothetical citation
can figure out which paper is the right one.

A reader may respond that,
if this was so easy,
*you* should have done it and put the results into the bibliography.
In response,
point out that shorter bibliography entries save paper;
claim that billions of trees are chopped down every year to print journals;
and accuse your reader of not caring about the environment.

[40] John B. Friedlander, Andrew Granville. Smoothing ``smooth'' numbers. Philosophical Transactions of the Royal Society of London Series A 345 (1993), 339-347. MR 95b:11086. http://www.dms.umontreal.ca/~andrew/Analytic.html.Given that URL, the reader can download a copy of the paper in far less time than it takes to visit the library.

If you're trying to slow the reader down, make sure you omit the URL:

[40] John B. Friedlander, Andrew Granville. Smoothing ``smooth'' numbers. Philosophical Transactions of the Royal Society of London Series A 345 (1993), 339-347. MR 95b:11086.This might do even more damage than ``[40] That old smoothing-smooth paper'': some readers, seeing the journal name, won't think of doing a Google search.

``Linkrot'' is a particularly serious problem for bibliography entries. I can update the links on this page (and did after my original link to http://www.math.uga.edu/~andrew/agpapers.html rotted), but I can't update the links in my psi paper in a printed volume.

Perhaps someday there will be a permanent URL for that paper,
suitable for citations,
such as http://cite.math.uga.edu/1993/granville.
But this doesn't mean that you have to use the permanent URL!
Even if you're forced to include *some* working URL,
you can encourage linkrot by choosing the URL
that appears least likely to survive past your publication date.

[17] P. Rogaway and D. Coppersmith, ``A software optimized encryption algorithm,'' Workshop on software encryption, Cambridge, 1993.The book containing the Rogaway-Coppersmith paper was not titled ``Workshop on software encryption'' and was not published in 1993. How is the reader supposed to find this book in his local library?

Here are some bad bibliography entries from other papers:

[27] R. Moenck and A. B. Borodin, Fast modular transforms via division, in Conf. Record, IEEE 13th Ann. Symposium on Switching and Automata Theory, 1972, pp. 90-96.Is ``Conf. Record, IEEE 13th Ann. Symposium on Switching and Automata Theory'' actually a book title? What does ``Proc. Symp. Pure Math.'' stand for? If the reader doesn't know, will the library catalog software be able to figure it out?[Sha71] D. Shanks. Class number, a theory of factorization and genera. In Proc. Symp. Pure Math. 20, pages 415-440. AMS, Providence, R.I., 1971.

Those bibliography entries could instead have been written as follows:

[1] Ross Anderson (editor). Fast software encryption. Lecture Notes in Computer Science 809. Springer-Verlag, Berlin, 1994. ISBN 3-540-58108-1. MR 97b:94004.Now the reader can easily look up the editor name and book title in the library's catalog. An ISBN search is even easier, if the catalog allows it, as most now do, and if the book has an ISBN. The series name and number make the book extremely easy to find in libraries that keep the series volumes together. The Math Reviews number gives MathSciNet subscribers another way to find information about the book.[2] Richard M. Karp (chairman). 13th annual symposium on switching and automata theory. IEEE Computer Society, Northridge, 1972.

[3] Donald J. Lewis (editor). 1969 Number Theory Institute. Proceedings of Symposia in Pure Mathematics 20. American Mathematical Society, Providence, 1971. ISBN 0-8218-1420-6. MR 47 #3286.

[4] Robert T. Moenck, Allan Borodin. Fast modular transforms via division. In [2] (1972), 90-96.

[5] Phillip Rogaway, Don Coppersmith. A software-optimized encryption algorithm. In [1] (1994), 56-63.

[6] Daniel Shanks. Class number, a theory of factorization, and genera. In [3] (1971), 415-440. MR 47 #4932.

Perhaps the library doesn't have the book. The reader may want to obtain the book from a nearby bookstore, an online bookstore, or the publisher. The editor name, book title, series name and number, publisher name, year, and ISBN help the reader locate the book and confirm that the book being purchased is the right one.

To prevent the reader from finding the book that you're citing, make sure that none of these mechanisms work.

[28] Allan Borodin, Robert T. Moenck. Fast modular transforms. Journal of Computer and System Sciences 8 (1974), 366-386. MR 51 #7365. Older version, not a subset, in [118].[93] Richard M. Karp (chairman). 13th annual symposium on switching and automata theory. IEEE Computer Society, Northridge, 1972.

[118] Robert T. Moenck, Allan Borodin. Fast modular transforms via division. In [93] (1972), 90-96. Newer version, not a superset, in [28].

Readers benefit in several ways from being able to find both versions of the paper:

- A reader looking for the 1972 paper might be able to retrieve the 1974 paper more easily, and vice versa. For most readers, either paper is adequate.
- Most of the results in the 1974 paper were already in the 1972 paper. Readers who want to properly assign credit will need to review the 1972 paper.
- Most of the results in the 1972 paper are explained more clearly and thoroughly in the 1974 paper. Readers who want to learn one of these results, and who have access to both papers, will prefer the 1974 paper.
- There are results that appear in the 1972 paper but not in the 1974 paper. Readers who want to learn everything will have to read both papers. (The Moenck-Borodin division algorithm was reinvented by two groups in 1998; it is not the same as the Borodin-Moenck division algorithm.) Of course, it would be nicer for the reader if the 1974 paper contained everything; but, since that isn't the case, the reader benefits from being able to find the 1972 paper too.

Readers may complain. In response, point out that citing both versions of the paper would fool citation indices into giving more credit to the authors, and would therefore encourage further redundancy in the permanent literature, which of course is the real problem.

Tellegen's theorem (13.20), a basic result in network theory, see, e.g., [142, 416, 9], says that transposing the K-DAG for a matrix A gives a K-DAG for its transpose.Presumably Buergisser et al. were looking at specific lines in [142], [416], and [9]. How is the reader supposed to find those lines?

I borrowed [142] from the library. It's an 867-page book by Desoer and Kuh titled ``Basic Circuit Theory.'' The index entry for Tellegen's theorem says ``393, 422-423; applications, 396-402, 807.'' Which of those 11 pages were Buergisser et al. referring to?

(The answer, as it turns out, is none of them. What Tellegen's theorem actually says is that the total power of an electrical circuit is 0. The idea of transposing circuits was introduced later by Bordewijk. But the citation's deceptiveness is a separate problem from its vagueness.)

To cause similar problems for your own readers, make sure to omit all page numbers, section numbers, etc. from your citations.