Properties of sets of nontransitive dice with few sides. (English) Zbl 1390.05039

Summary: We define and investigate several properties that sets of nontransitive dice might have. We prove several implications between these properties, which hold in general or for dice with few sides. We also investigate some algorithms for creating sets of 3-sided dice that realize certain tournaments.


05B30 Other designs, configurations
05C20 Directed graphs (digraphs), tournaments
60C05 Combinatorial probability
Full Text: DOI


[1] 10.1002/jcd.21563 · Zbl 1377.05073
[2] ; Bednay, Proceedings of the 8th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications, 15 (2013)
[3] ; Bozóki, Miskolc Math. Notes, 15, 39 (2014)
[4] 10.1038/scientificamerican1270-110
[5] 10.2307/2974903 · Zbl 0808.05011
[6] 10.4169/college.math.j.48.1.10 · Zbl 1443.97048
[7] ; Steinhaus, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 7, 67 (1959)
[8] 10.4064/am-5-4-321-332
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