On round-robin tournaments with a unique maximum score
| dc.contributor.author | Malinovsky, Yaakov | |
| dc.contributor.author | Moon, John W. | |
| dc.date.accessioned | 2022-10-13T14:32:15Z | |
| dc.date.available | 2022-10-13T14:32:15Z | |
| dc.date.issued | 2024 | |
| dc.description.abstract | Richard Arnold Epstein (1927–2016) published the first edition of “The Theory of Gambling and Statistical Logic” in 1967. He introduced some material on round-robin tournaments (complete oriented graphs) with n labeled vertices in Chapter 9; in particular, he stated, without proof, that the probability that there is a unique vertex with the maximum score tends to 1 as n tends to infinity. Our goal here is to give a proof of this result along with some historical remarks and comments. | en_US |
| dc.description.sponsorship | We thank Noga Alon for referring us to the work of Paul Erd˝os and Robin J. Wilson. We also thank Boris Alemi for executing the Maple program on a powerful computer and obtaining the data in the required format. The research of YM was supported by grant no. 2020063 from the United States–Israel Binational Science Foundation (BSF). | en_US |
| dc.description.uri | https://ajc.maths.uq.edu.au/pdf/89/ajc_v89_p024.pdf | en_US |
| dc.format.extent | 8 pages | en_US |
| dc.genre | journal articles | en_US |
| dc.identifier | doi:10.13016/m2bdef-rdt9 | |
| dc.identifier.citation | Malinovsky, Yaakov, and John W Moon. “On Round-Robin Tournaments with a Unique Maximum Score.” AUSTRALASIAN JOURNAL OF COMBINATORICS 89, no. 1 (2024): 24–31. https://ajc.maths.uq.edu.au/pdf/89/ajc_v89_p024.pdf | |
| dc.identifier.uri | http://hdl.handle.net/11603/26168 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | The University of Queensland | |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mathematics Department Collection | |
| dc.relation.ispartof | UMBC Faculty Collection | |
| dc.rights | Attribution 4.0 International | en_US |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/deed.en | |
| dc.title | On round-robin tournaments with a unique maximum score | en_US |
| dc.title.alternative | On Round-Robin Tournaments with a Unique Maximum Score and Some Related Results | |
| dc.type | Text | en_US |
| dcterms.creator | https://orcid.org/0000-0003-2888-674X | en_US |