Partial order on a family of κ-subsets of a linearly ordered set
College
College of Science
Department/Unit
Mathematics and Statistics Department
Document Type
Article
Source Title
Discrete Mathematics
Volume
306
Issue
4
First Page
413
Last Page
419
Publication Date
3-6-2006
Abstract
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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Digitial Object Identifier (DOI)
10.1016/j.disc.2005.12.018
Recommended Citation
Gervacio, S. V., & Maehara, H. (2006). Partial order on a family of κ-subsets of a linearly ordered set. Discrete Mathematics, 306 (4), 413-419. https://doi.org/10.1016/j.disc.2005.12.018
Disciplines
Mathematics
Keywords
Acyclic models; Cycles
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