Partial order on a family of κ-subsets of a linearly ordered set
For k-subsets A,B of the rationals Q, define A≻nB if a>b holds for at least n ordered pairs (a,b)∈A×B, where k,n are integers, 1≤n≤k2. We prove that (1) the relation ≻n is transitive if and only if k2-k+1≤n, and (2) there is a cyclic sequence A1≻nA2≻n⋯≻ nAr≻nA1 of k-subsets of Q if and only if 1≤...
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2006
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oai:animorepository.dlsu.edu.ph:faculty_research-23712021-06-23T07:24:08Z Partial order on a family of κ-subsets of a linearly ordered set Gervacio, Severino V. Maehara, Hiroshi For k-subsets A,B of the rationals Q, define A≻nB if a>b holds for at least n ordered pairs (a,b)∈A×B, where k,n are integers, 1≤n≤k2. We prove that (1) the relation ≻n is transitive if and only if k2-k+1≤n, and (2) there is a cyclic sequence A1≻nA2≻n⋯≻ nAr≻nA1 of k-subsets of Q if and only if 1≤n≤k2-⌊(k+1)2/ 4⌋. We also investigate the length of such cyclic sequences. © 2006 Elsevier B.V. All rights reserved. 2006-03-06T08:00:00Z text text/html https://animorepository.dlsu.edu.ph/faculty_research/1372 https://animorepository.dlsu.edu.ph/context/faculty_research/article/2371/type/native/viewcontent Faculty Research Work Animo Repository Acyclic models Cycles Mathematics |
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Acyclic models Cycles Mathematics |
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Acyclic models Cycles Mathematics Gervacio, Severino V. Maehara, Hiroshi Partial order on a family of κ-subsets of a linearly ordered set |
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For k-subsets A,B of the rationals Q, define A≻nB if a>b holds for at least n ordered pairs (a,b)∈A×B, where k,n are integers, 1≤n≤k2. We prove that (1) the relation ≻n is transitive if and only if k2-k+1≤n, and (2) there is a cyclic sequence A1≻nA2≻n⋯≻ nAr≻nA1 of k-subsets of Q if and only if 1≤n≤k2-⌊(k+1)2/ 4⌋. We also investigate the length of such cyclic sequences. © 2006 Elsevier B.V. All rights reserved. |
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text |
| author |
Gervacio, Severino V. Maehara, Hiroshi |
| author_facet |
Gervacio, Severino V. Maehara, Hiroshi |
| author_sort |
Gervacio, Severino V. |
| title |
Partial order on a family of κ-subsets of a linearly ordered set |
| title_short |
Partial order on a family of κ-subsets of a linearly ordered set |
| title_full |
Partial order on a family of κ-subsets of a linearly ordered set |
| title_fullStr |
Partial order on a family of κ-subsets of a linearly ordered set |
| title_full_unstemmed |
Partial order on a family of κ-subsets of a linearly ordered set |
| title_sort |
partial order on a family of κ-subsets of a linearly ordered set |
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Animo Repository |
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2006 |
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https://animorepository.dlsu.edu.ph/faculty_research/1372 https://animorepository.dlsu.edu.ph/context/faculty_research/article/2371/type/native/viewcontent |
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