This is the abstract of a poster presented at the International Symposium on Symbolic and Algebraic Computation (ISSAC) 2014 dealing with Gaussian elimination over a ring R, and hence “fraction free,” that is, not working in the field of quotients. The paper states:

In particular, we set out to confirm popular beliefs about fraction-free methods. For instance, [1] remarks (without any further source or proof) that the preferred pivoting strategy in symbolic Gaussian elimination as opposed to numerical methods is to choose always the smallest possible pivot (with a suitable measure of size depending on R). Our experiments confirmed that this strategy leads to the smallest output.

Unfortunately, this paper also contains no source or proof, and the experimental results are not given. In this day and age, an abstract of a poster should at least contain a link to the original poster.

The authors extend their observation in [2] that even using the Bareiss-Dodgson method, which removes all structural common factors, there are still many more common factors in any example than one would reasonably expect. This is, as they say, a promising area for future research.