Talk:Sparse ruler

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I have created this page as a starting point for this subject. Puzzles about sparse rulers have appeared in puzzle columns for decades. I am hoping that others with specific expertise in this area will expand the article. I would especially appreciate references from print sources, rather than just webpages. Contestcen (talk) 04:46, 16 May 2009 (UTC)[reply]

I added examples, but I hope I did not make the page too cluttered. Most were examples I found (full list here: [1]). The topic of Wichmann rulers and the identification of some of the larger optimal rulers came from [2].

I remember first reading about these in a Martin Gardner book, though I cannot remember which one. Wnmyers (talk) 20:45, 8 August 2009 (UTC)[reply]

Unclear definition of minimal ruler

The current page says "A sparse ruler is called minimal if there is no sparse ruler of length L with m-1 marks. In other words, if any of the marks is removed one can no longer measure all of the distances." But these two sentences seem to define different things. The first says that any arrangement of m-1 marks will not be a sparse ruler, while the second says that removing any of the m marks (without moving the others) will not be a sparse ruler. Looking at the references, I cannot tell which is the correct (or more common) definition, so I have added a clarification needed tag. Mnudelman (talk) 14:59, 16 September 2013 (UTC)[reply]

I reworded the description and I hope it is clearer. I also changed it to more closely match Peter Luschny's definition. A sparse ruler is now any ruler, and a complete ruler is what this page used to call a sparse ruler. I also moved a table of incomplete rulers from the "Perfect ruler" page to a section here, where it seems to match the definition better. Wnmyers (talk) 06:15, 16 December 2013 (UTC)[reply]

Updating Asymptotics

Some of the asymptotics could be removed now that a tight upper bound is proven with constructions.EdPeggJr (talk) 21:07, 6 July 2020 (UTC)[reply]

While I agree that Wichmann's result from 1964 means we can update the upper bound, I disagree strongly with several of the other additions to this page, and I am going to take the liberty to change some of them in a moment. There are well-established and strongly worded Wikipedia policies against referring to your own self-published research: see for example https://en.wikipedia.org/wiki/Wikipedia:Reliable_sources#Self-published_sources_(online_and_paper) or https://en.wikipedia.org/wiki/Wikipedia:No_original_research. If you believe you have novel contributions to this body of research, I would strongly suggest that you persue the usual approach of submitting them to a mathematical journal for traditional peer review (or at the very least to the arXiv for crowd review). I hope you do not feel I am being rude about the obvious effort you have put in to studying these fascinating objects. --Sean Eberhard (talk) 16:17, 27 July 2025 (UTC)[reply]

I mostly compiled results (A326499: [3]) and identified a few hundred alternate Wichmann constructions. For compiled results, OEIS is often sufficient. Brian Wichmann's upper bound is the same as the Excess formula (derived from his construction). His paper argued that the Excess could be up to 3. It turns out that the Excess is always 1 or 0. — Preceding unsigned comment added by EdPeggJr (talk • contribs) 19:20, 27 July 2025 (UTC)[reply]