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I'm searching for a copy of an old paper made by Edmund Landau:

Zur relativen Wertbemessung der Turnierresultate, Deutsches Wochenschach, 11. Jahrgang (1895), 366–369.

However, I can't find it anywhere. I looked at some old books written by Landau and did not succeed in my quest.

The Princeton University has the volume 50-1895 of the magazine "Deutsche Schachzeitung" where this paper should appear: HathiTrust record.

Landau published this early work in a Chess magazine. However, it seems to be that paper has several implications in the theory of Ranking and positive matrices and worked as a motivation for the next works of Landau.

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  • $\begingroup$ Perhaps you can find help from a librarian. Tracking down old materials is part of their expertise. $\endgroup$
    – Ovi
    Aug 11, 2020 at 16:21
  • $\begingroup$ I'm thinking about that. Perhaps some big and old library has the book where this article was published. However, I don't know how can I achieve that. I'm just a student in Brazil. $\endgroup$
    – daemon
    Aug 11, 2020 at 16:47
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    $\begingroup$ Right, but I think your university librarians might have a way to help. Libraries are often part of international networks which allow them to share books with each other. One such network is WorldCat worldcat.org You can try going through them yourself, but in any case, remember that librarians have masters or PhD's in Library Science, so they really know a lot. $\endgroup$
    – Ovi
    Aug 11, 2020 at 17:19
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    $\begingroup$ You probably know this already, but E. Landau seems to have written more about the topic in "Zeitschrift für Mathematik und Physik“ , vol. 63, pages 192-208. That is one famous issue because of a certain A. Einstein a few pages later. $\endgroup$
    – user114668
    Aug 11, 2020 at 23:11
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    $\begingroup$ You could also try to ask at chess.stackexchange.com , $\endgroup$ Oct 13, 2020 at 18:01

2 Answers 2

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The paper which actually was Landau's first scientific paper written at the tender age of 18, was published in his Collected Works, vol. 1. In it, he proposes to rank chess players having played a round robin tournament according to an eigenvector of the results matrix . A much more comprehensive analysis of this method with the help of the (then new) Perron-Frobenius theorem is given in his 1915 paper "Über Preisverteilung bei Spielturnieren", to be found in his Collected Works, vol. 6. The latter paper can be downloaded here: https://iris.univ-lille.fr/handle/1908/2031

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  • $\begingroup$ It seems very hard to get a copy from this Collected Works . But I'm happy now with this 1915 paper. Thanks. It's sad, those papers deserves an english translation. $\endgroup$
    – daemon
    Nov 30, 2021 at 2:02
  • $\begingroup$ The introduction of his 1915 paper is a restatement of his earlier paper, i.e. the proposal to rate the players according to an eigenvector of the results matrix, which in chess contains the values 1, 1/2 and 0. In §1 he says that all is well if the results matrix is irreducible. §2 shows the possibility of a nonunique rating if the matrix is reducible. In §3 he shows that in certain cases inconsistencies can occur, namely that the score of a player can decrease if the outcome of a certain match is changed in his or her favor, which ultimately leads him to reject his own method. $\endgroup$ Nov 30, 2021 at 13:27
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If you have an account in springer you can see here:

https://link.springer.com/chapter/10.1007%2F978-1-4615-4819-5_23

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  • $\begingroup$ It's a great compendium about some works of E. Landau. However, "Zur relativen Wertbemessung der Turnierresultate" was not published in this chapter $\endgroup$
    – daemon
    Nov 30, 2021 at 1:54

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