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Re: [HM] Fleury's algorithm
Posted:
Nov 28, 2004 5:33 PM


On 16 Apr 2002, Margherita Barile wrote some information about Fleury and his algorithm, and on 1 Jan 2003, Adam Drozdek provided a correction. Barile says "Edouard Lucas, in his book "Recreations Mathematiques" (appeared for the first time in Paris in 1891), refers to a certain "M. Fleury" as a "chief of institution" from Marseille who published his algorithm in the note "Deux problemes de geometrie de situation", published in a 1885 issue of the French periodical "Journal de mathematiques Elementaires". He gives page 257 as a reference. I, however, could not find this page." I have done a little searching and I have a number of comments. Lucas's book has four volumes. Vol. 1 appeared in 1883, with a 2nd ed. in 1891. Vol. 2 appeared in 1883 with a second edition in 1893(?). Vols. 3 & 4 appeared in 1893 & 1894, and never had second editions. The currently available reprint series uses the 2nd ed. of vol. 1 and the 1st ed. of vol. 2. I have never observed any significant differences in the editions of vol. 2, but I have not seen a copy of the 1st ed. of vol. 1. Lucas's books (like all too many 19C works) are notorious for not having indexes. Consequently a reference without a volume and page is a real pain to try to track down, especially for a topic like Fleury's algorithm which might occur in a number of different places. So far as I can tell, Fleury is not mentioned in the 2nd ed. of vol. 1, EXCEPT that his paper Deux proble\mes de Ge/ome/trie de situation in Journal de Math. e/le/m. is listed on p. 247, but with year 1885, which Drozdek corrects to 1883. [e/ is e with an accent acute; e\ is e with accent grave.] Fleury is cited extensively in vol. 4, pp. 240254, which describes him as the inventor of a number of games, some of which were previously described in vol. 3, pp. 87103, but he is not mentioned there. None of the references above say that Fleury was a "chief of institution" from Marseille. For material of this period, one of the best sources is Wilhelm Ahrens' Mathematische Unterhaltungen und Spiele, 2 vols., 2nd ed. 1910, 1918 (publication was interrupted by WW1; there is a 1921 3rd ed of vol. 1, but it has only some corrections made and 2pp of extra notes). He has a bibliography of 762 items and a thorough index which cites Fleury twice and two of his papers (a misprint cites another paper). In vol. 2, p. 231, in a long footnote on the Fifteen Puzzle, Ahrens cites an 1880 paper of Fleury (no. 374 in his bibliography), which he has not seen. In vol. 2, p. 239, in a footnote on the question of parity in the Fifteen Puzzle, Ahrens notes that the use of two identical pieces makes all positions solvable, as in the variant French game invented by Fleury and named Came/le/on. Ahrens refers to Lucas, vol. 3, pp. 8999, 155158 (I don't see anything relevant on the latter pages, but perhaps this was another of Fleury's games), to vol. 4, pp. 240254 and to two papers of Fleury in Interme/diaire des mathe/maticiens, 1 (1894) 215216 (cf p. 35) [item 524 in the bibliography] and 5 (1898) 159160 (cf p. 28). Not having seen these, I'm not quite sure why he has added the cfs. In vol. 2, p. 403 has the bibliographic item 374: Fleury, H. "La cle/ du taquin, ou la solution des quinze." Marseille, 1880. In vol. 2, p. 414 has the item 524: Fleury, Henry. [U"ber das "Chama"leon" und verwandte Spiele.] Interme/d. des mathe/m. 1, 1894, p. 215216. [Here U" denotes U with an umlaut and a" denotes a with an umlaut.]
Hope this is of some use. David Singmaster



