A Direct Construction of Nontransitive Dice Sets
In this paper, we give a direct construction for a set of dice realizing any given tournament T . The construction for a tournament with n vertices requires dice with n sides if n is odd, n + 1 sides if n is divisible by 4, and n − 1 sides if n ≡ 2 mod 4. This appears to be the most efficient genera...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Angel, Levi [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Rechteinformationen: |
Nutzungsrecht: © 2017 Wiley Periodicals, Inc. |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Journal of combinatorial designs - New York, NY : Wiley, 1993, 25(2017), 11, Seite 523-529 |
|---|---|
| Übergeordnetes Werk: |
volume:25 ; year:2017 ; number:11 ; pages:523-529 |
| Links: |
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| DOI / URN: |
10.1002/jcd.21563 |
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| 520 | |a In this paper, we give a direct construction for a set of dice realizing any given tournament T . The construction for a tournament with n vertices requires dice with n sides if n is odd, n + 1 sides if n is divisible by 4, and n − 1 sides if n ≡ 2 mod 4. This appears to be the most efficient general construction to date. Our construction relies only on a standard construction from graph theory. | ||
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10.1002/jcd.21563 doi PQ20171228 (DE-627)OLC1998285685 (DE-599)GBVOLC1998285685 (PRQ)p1043-427938e5f554cfffdcc50f571ace1206a792acdab3643c6aa71edab902c9960b3 (KEY)0227317920170000025001100523directconstructionofnontransitivedicesets DE-627 ger DE-627 rakwb eng 004 DE-600 Angel, Levi verfasserin aut A Direct Construction of Nontransitive Dice Sets 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In this paper, we give a direct construction for a set of dice realizing any given tournament T . The construction for a tournament with n vertices requires dice with n sides if n is odd, n + 1 sides if n is divisible by 4, and n − 1 sides if n ≡ 2 mod 4. This appears to be the most efficient general construction to date. Our construction relies only on a standard construction from graph theory. Nutzungsrecht: © 2017 Wiley Periodicals, Inc. nontransitive dice Graph theory Construction standards Construction Davis, Matt oth Enthalten in Journal of combinatorial designs New York, NY : Wiley, 1993 25(2017), 11, Seite 523-529 (DE-627)171284372 (DE-600)1173570-3 (DE-576)03873298X 1063-8539 nnns volume:25 year:2017 number:11 pages:523-529 http://dx.doi.org/10.1002/jcd.21563 Volltext http://onlinelibrary.wiley.com/doi/10.1002/jcd.21563/abstract https://search.proquest.com/docview/1937315349 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_70 GBV_ILN_2244 AR 25 2017 11 523-529 |
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10.1002/jcd.21563 doi PQ20171228 (DE-627)OLC1998285685 (DE-599)GBVOLC1998285685 (PRQ)p1043-427938e5f554cfffdcc50f571ace1206a792acdab3643c6aa71edab902c9960b3 (KEY)0227317920170000025001100523directconstructionofnontransitivedicesets DE-627 ger DE-627 rakwb eng 004 DE-600 Angel, Levi verfasserin aut A Direct Construction of Nontransitive Dice Sets 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In this paper, we give a direct construction for a set of dice realizing any given tournament T . The construction for a tournament with n vertices requires dice with n sides if n is odd, n + 1 sides if n is divisible by 4, and n − 1 sides if n ≡ 2 mod 4. This appears to be the most efficient general construction to date. Our construction relies only on a standard construction from graph theory. Nutzungsrecht: © 2017 Wiley Periodicals, Inc. nontransitive dice Graph theory Construction standards Construction Davis, Matt oth Enthalten in Journal of combinatorial designs New York, NY : Wiley, 1993 25(2017), 11, Seite 523-529 (DE-627)171284372 (DE-600)1173570-3 (DE-576)03873298X 1063-8539 nnns volume:25 year:2017 number:11 pages:523-529 http://dx.doi.org/10.1002/jcd.21563 Volltext http://onlinelibrary.wiley.com/doi/10.1002/jcd.21563/abstract https://search.proquest.com/docview/1937315349 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_70 GBV_ILN_2244 AR 25 2017 11 523-529 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a2200265 4500</leader><controlfield tag="001">OLC1998285685</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230715081515.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">171125s2017 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1002/jcd.21563</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">PQ20171228</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC1998285685</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)GBVOLC1998285685</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(PRQ)p1043-427938e5f554cfffdcc50f571ace1206a792acdab3643c6aa71edab902c9960b3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(KEY)0227317920170000025001100523directconstructionofnontransitivedicesets</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">004</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Angel, Levi</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="2"><subfield code="a">A Direct Construction of Nontransitive Dice Sets</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2017</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In this paper, we give a direct construction for a set of dice realizing any given tournament T . 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