The diamond lemma has recently come up in my teaching, and as always I've been looking for nice and simple applications. This has reminded me of the thesis

Kimmo Eriksson, Strongly convergent games and Coxeter groups, KTH Stockholm 1993,

which I have never been able to locate despite the existence of a ProQuest page and many (Google Scholar says 60) citations in the literature.

Does anyone have a scan of this thesis? (I am aware of several papers by Eriksson, but I'm not sure how much of the thesis they cover.)

  • $\begingroup$ Is there a particular result you're interested in that you believe is contained in this thesis? $\endgroup$ Commented Jun 29, 2022 at 16:31
  • $\begingroup$ @SamHopkins: I'm hoping for more elementary applications to use in my lecture :) $\endgroup$ Commented Jun 29, 2022 at 16:39
  • $\begingroup$ Have you tried writing to Kimmo? I'm sure that if anyone has a copy, it's him. (As an aside, Kimmo's father Henrik did a PhD in 1994, also at KTH and on a similar topic, and this thesis is available here). $\endgroup$ Commented Jun 29, 2022 at 22:47
  • $\begingroup$ Also, if you want nice and simple applications of the diamond lemma, it is used all the time in string rewriting systems and combinatorial (semi)group theory. The easiest application is to show that the bicyclic monoid has decidable word problem; or that free groups are well-defined as the group of all freely reduced words with multiplication given by concatenation, followed by reducing. $\endgroup$ Commented Jun 29, 2022 at 22:53
  • 1
    $\begingroup$ An application of the diamond lemma to enumeration can be found in the proof of Theorem 4.4 in my paper with Ji Li, Enumeration of point-determining graphs, J. Combin. Theory Ser. A 118 (2011), 591–612, doi.org/10.1016/j.jcta.2010.03.009. $\endgroup$
    – Ira Gessel
    Commented Dec 9, 2022 at 18:48

1 Answer 1


The thesis can now be found at https://archive.org/details/eriksson-strongly-convergent-games-thesis .

Thanks to Kimmo Eriksson for sending me a hard copy and allowing it to be shared!


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