I would like to collect examples of errors in published numerical results in computational combinatorics: where a result (typically a counting of some objects, or an extremal quantity within some large class of objects) was published, but later found to be incorrect.
My motivation here is to better understand the extent, and especially, the kinds of errors that happen, and to understand what would be good methods to avoid them. Personally I have seen a few examples, but my understanding is that such errors are in fact surprisingly rare. (One might ask whether this is because these errors happen rarely, or because they are noticed rarely.) What makes such errors nasty is that they may be very difficult to notice.
Some clarifications of what I am after:
It should be a definitely erroneous result, not just an oversight in a definition or something like that (e.g. forgetting to say "oh, we mean nonempty").
The result apparently comes from a substantial amount of computation (let's say at least 1 cpu hour, but I am not particular), and from the publication itself, it is well nigh impossible for the reader to notice the error, without e.g. doing the computations again.
The published result itself should be erroneous, not just some correctable details in its proof or the computations that led to the result.
The cause of the error could be in hardware, mistake in algorithm, programming error, human error in processing the results, or even unknown. Please mention if the cause is known.
The erroneous result and its correction were both stated in a scientific publication (book, journal, conference proceedings; even arXiv manuscript OK if you think that it is creditable). This excludes e.g. corrections to OEIS entries [mainly because they are relatively common, and because their documentation is often quite terse, as in "a(4) corrected by me, that's it"].
I'm not looking for improvements of lower bounds, disproofs of conjectures etc. but corrections of factual errors.
An example to clarify what I am seeking:
Heitzig and Reinhold (2002) counted unlabeled lattices of up to 18 elements, and wrote: "We are sure that Koda’s values for $l(12)$ and $l(13)$ are wrong." Koda (1992) counted 262775 and 2018442, H&R counted 262776 and 2018305. There is no indication of the cause of the discrepancy.
Reference: Heitzig, Jobst; Reinhold, Jürgen, Counting finite lattices., Algebra Univers. 48, No. 1, 43-53 (2002). ZBL1058.05002.
For contrast, here are some other MO questions about errors and computation:
- How can we be sure that results that rely heavily on extensive computations are correct?
- Computer algebra errors
- How do I fix someone's published error?
- Diplomacy when reporting errors
I am requesting this to be CW because obviously there is not a single correct answer.