Zigzags of Finite, Bounded Posets and Monotone Near-Unanimity Functions and Jónsson Operations

Zigzags;Monotone Near-unanimity functions;Monotone Jónsson operations;Zadori"s conjecture;Pure Mathematics

Martin, Eric

University of Waterloo

关键词: Zigzags;    Monotone Near-unanimity functions;    Monotone Jónsson operations;    Zadori";    s conjecture;    Pure Mathematics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/4730/1/uwthesis.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

We define the notion of monotone operations admitted by partially ordered sets,specifically monotone near-unanimity functions and Jónsson operations. We thenprove a result of McKenzie;;s in [8] which states that if a finite, bounded poset Padmits a set of monotone Jónsson operations then it admits a set of monotoneJónsson operations for which the operations with even indices do not depend ontheir second variable. We next define zigzags of posets and prove various usefulproperties about them. Using these zigzags, we proceed carefully through Zadori;;sproof from [12] that a finite, bounded poset P admits a monotone near-unanimityfunction if and only if P admits monotone Jónsson operations.