2006/06/01 by Ján Jakubík · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #semigroups and automata theory #Mathematics #Combinatorics #Monotone polygon #Order (exchange) #Ternary operation #Set (abstract data type) #Partially ordered set #Bar (unit) #Cyclic group #Total order #Group (periodic table) #Ordered set #Rank (graph theory) #Discrete mathematics #Abelian group #Geometry #Physics #Computer science
paper · doi:10.1007/s10587-006-0026-4
openalex publication_date 2006/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
For an ℓ-cyclically ordered set M with the ℓ-cyclic order C let P(M) be the set of all monotone permutations on M. We define a ternary relation C on the set P(M). Further, we define in a natural way a group operation (denoted by ·) on P(M). We prove that if the ℓ-cyclic order C is complete and C ≠ 0, then (P(M),·, C ) is a half cyclically ordered group.