Partial order on a family of κ-subsets of a linearly ordered set

• Main Authors: Gervacio, Severino V., Maehara, Hiroshi
• Format: text
• Published: Animo Repository 2006
• Subjects: Acyclic models; Cycles; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/faculty_research/1372; https://animorepository.dlsu.edu.ph/context/faculty_research/article/2371/type/native/viewcontent
• Institution: De La Salle University

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≤...