most recent 30 from http://mathoverflow.net 2013-05-24T13:31:01Z http://mathoverflow.net/feeds/question/47044 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/47044/what-are-some-early-examples-of-creation-of-lists-catalogues-of-particularly gordon-royle 2010-11-23T02:30:52Z 2010-11-23T23:22:17Z

<p>A lot of effort in discrete maths / combinatorics is expended in the construction of lists, catalogues or census [sic] of combinatorial objects such as groups, graphs, designs etc. These catalogues are now a fundamental part of computer algebra systems.</p> <p>Obviously nowadays most of this is done by computer, but a surprisingly large amount of this work predates (electronic) computers - for example, G.A. Miller worked on creating lists of "substitution groups" (permutation groups) in the late 1800s and early 1900s, while Ronald Foster created the "Foster Census" of cubic symmetric graphs in the 1930s.</p> <p>I'd like to know some more examples of famous "cataloguers" of mathematical (well, particularly combinatorial) objects predating electronic computers. </p>

http://mathoverflow.net/questions/47044/what-are-some-early-examples-of-creation-of-lists-catalogues-of-particularly/47045#47045 Daniel Geisler 2010-11-23T02:48:09Z 2010-11-23T02:48:09Z

<p>Ernst Schroeder's 1870 paper "Vier combinatorische Probleme" discusses four closely related combinatorial structures.</p>

http://mathoverflow.net/questions/47044/what-are-some-early-examples-of-creation-of-lists-catalogues-of-particularly/47047#47047 Richard Stanley 2010-11-23T03:14:19Z 2010-11-23T23:22:17Z

<p>Donald Knuth has lots of interesting information on the history of the generation of basic combinatorial objects such as partitions and permutations in Section 7.2.1.7 of <em>The Art of Computer Programming</em>, vol. 4, Fascicle 4. The enumeration of the 318 6-element posets up to isomorphism appears in the 1972 Ph.D. thesis of John A. Wright. </p> <p><strong>Update.</strong> Diagrams depicting the 52 partitions of a 5-element set were used as chapter headings for all but the first and last chapter of certain editions of <em>The Tale of Genji</em> by Lady Murasaki (c. 978-c. 1031 CE), beginning in the seventeenth century. See <a href="http://en.wikipedia.org/wiki/File:Genji_chapter_symbols_groupings_of_5_elements.svg" rel="nofollow">http://en.wikipedia.org/wiki/File:Genji_chapter_symbols_groupings_of_5_elements.svg</a>.</p>

http://mathoverflow.net/questions/47044/what-are-some-early-examples-of-creation-of-lists-catalogues-of-particularly/47052#47052 Gerry Myerson 2010-11-23T05:18:09Z 2010-11-23T05:18:09Z

<p>Catalogs of prime numbers and of factorizations of composites long predate electronic computers. The following information is taken from Table 85 on page 218 of Albert H Beiler, Recreations in the Theory of Numbers, Dover, 1964. </p> <p>Lists of primes. Up to 97, L Pisano, 1202. 750, P Cataldi, 1603. 10,000, F van Schooten, 1657. 100,999, J G Kruger, 1746. 102,000, J H Lambert, 1770. 400,000, A F Marci, 1772. 10,000,000, D N Lehmer, 1914. </p> <p>Factor tables. Up to 100, Pisano, 1202. 800, Cataldi, 1603. 24,000, J H Rahn, 1659. 100,000, T Brancker, 1668. 2,856,000, A Felkel, 1785. 3,000,000, J C Burckhardt, 1814-1817. 7,000,000 to 9,000,000, Z Dase and H Rosenberg, 1862-3. 100,000,000, J P Kulik, 1867. 3,000,000 to 6,000,000, J Glaisher, 1879-83. 10,000,000, D N Lehmer, 1909. </p> <p>Not clear to me what purpose the factor tables of Glaisher and Lehmer served, when Kulik had already gone much farther, but I'm sure there's some explanation. </p> <p>Also, I'm guessing Beiler got his information from Dickson's History. </p>

http://mathoverflow.net/questions/47044/what-are-some-early-examples-of-creation-of-lists-catalogues-of-particularly/47053#47053 Gerry Myerson 2010-11-23T05:26:28Z 2010-11-23T05:40:25Z

<p>Pre-computer lists of knots (from a mathematical point of view) go back to Listing, 1847, followed by the work of Tait, Kirkman, and Little (I don't have the exact dates, but late 19th century, I suppose). Also M G Haseman (early 20th century, I think). </p> <p>EDIT: I found a few references: J.-B. Listing, Vorstudien zur topologie, Goettinger Studien 1 (1847) 811–875.</p> <p>M. Haseman, On knots, with a census of the amphicheirals with twelve crossings, Trans. Roy. Soc. Edinburgh 52 (1918) 235–255.</p>

http://mathoverflow.net/questions/47044/what-are-some-early-examples-of-creation-of-lists-catalogues-of-particularly/47054#47054 Gerry Myerson 2010-11-23T05:48:34Z 2010-11-23T05:48:34Z

<p>Tutte had a series of papers that may qualify: </p> <p>MR0130841 (24 #A695) Tutte, W. T. A census of planar triangulations. Canad. J. Math. 14 1962 21–38. </p> <p>MR0137657 (25 #1108) Tutte, W. T. A census of Hamiltonian polygons. Canad. J. Math. 14 1962 402–417. </p> <p>MR0142470 (26 #39) Tutte, W. T. A census of slicings. Canad. J. Math. 14 1962 708–722. </p> <p>MR0146823 (26 #4343) Tutte, W. T. A census of planar maps. Canad. J. Math. 15 1963 249–271. </p> <p>In Figure 8 of the last paper, he illustrates the rooted bicubic maps with $2n$ vertices for $n\le4$, according to the review by G. de B. Robinson. </p>

http://mathoverflow.net/questions/47044/what-are-some-early-examples-of-creation-of-lists-catalogues-of-particularly/47055#47055 Gerry Myerson 2010-11-23T06:02:19Z 2010-11-23T06:02:19Z

<p>Frenicle de Bessy is credited with enumerating the 880 magic squares of order 4 in 1693. I don't know whether he actually listed them all. The reference, as given at MathWorld, is Frénicle de Bessy, B. "Des quarrez ou tables magiques. Avec table generale des quarrez magiques de quatre de costé." In Divers Ouvrages de Mathématique et de Physique, par Messieurs de l'Académie Royale des Sciences (Ed. P. de la Hire). Paris: De l'imprimerie Royale par Jean Anisson, pp. 423-507, 1693. Reprinted as Mem. de l'Acad. Roy. des Sciences 5 (pour 1666-1699), 209-354, 1729.</p>

http://mathoverflow.net/questions/47044/what-are-some-early-examples-of-creation-of-lists-catalogues-of-particularly/47065#47065 Gerry Myerson 2010-11-23T07:57:26Z 2010-11-23T07:57:26Z

<p>MacMahon computed the number of partitions of $n$ for $n\le200$, roughly 100 years ago (sorry, don't have the exact citation). </p>

http://mathoverflow.net/questions/47044/what-are-some-early-examples-of-creation-of-lists-catalogues-of-particularly/47068#47068 Martin Rubey 2010-11-23T08:06:54Z 2010-11-23T08:06:54Z

<pre> @book {MR0357292, AUTHOR = {Sloane, N. J. A.}, TITLE = {A handbook of integer sequences}, PUBLISHER = {Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London}, YEAR = {1973}, PAGES = {xiii+206}, MRCLASS = {10A40 (05AXX 65A05)}, MRNUMBER = {0357292 (50 \#9760)}, } </pre> <p>It is a predecessor of the <a href="http://oeis.org/" rel="nofollow">online encyclopedia of integer sequences</a>, of course. As intermediate step, there is the sequel</p> <pre> @book {MR1327059, AUTHOR = {Sloane, N. J. A. and Plouffe, Simon}, TITLE = {The encyclopedia of integer sequences}, NOTE = {With a separately available computer disk}, PUBLISHER = {Academic Press Inc.}, ADDRESS = {San Diego, CA}, YEAR = {1995}, PAGES = {xiv+587}, ISBN = {0-12-558630-2}, MRCLASS = {11-00 (05A10 11B83 11Y55)}, MRNUMBER = {1327059 (96a:11001)}, MRREVIEWER = {P{\'e}ter Kiss}, } </pre>

http://mathoverflow.net/questions/47044/what-are-some-early-examples-of-creation-of-lists-catalogues-of-particularly/47156#47156 Ursula Martin 2010-11-23T22:34:19Z 2010-11-23T22:53:23Z

<p>Hall, Jr., Marshall; Senior, James K. (1964), The Groups of Order $2^n$ (n ≤ 6), Macmillan, LCCN 64-16861, MR168631. </p> <p>This is a catalog of the 340 groups of order dividing 64 with detailed tables of defining relations, constants, and lattice presentations of each group. It is extremely large (A2 size?), and hence often lurks in an odd place in libraries looking battered and sorry for itself.</p>