Memoirs of the American Mathematical Society 1997; 166 pp; softcover Volume: 129 ISBN10: 082180622X ISBN13: 9780821806227 List Price: US$54 Individual Members: US$32.40 Institutional Members: US$43.20 Order Code: MEMO/129/614
 The class of cyclefree partial orders (CFPOs) is defined, and the CFPOs fulfilling a natural transitivity assumption, called \(k\)connected set transitivity (\(k\)\(CS\)transitivity), are analyzed in some detail. Classification in many of the interesting cases is given. This work generalizes Droste's classification of the countable \(k\)transitive trees (\(k \geq 2\)). In a CFPO, the structure can branch downwards as well as upwards, and can do so repeatedly (though it never returns to the starting point by a cycle). Mostly it is assumed that \(k \geq 3\) and that all maximal chains are finite. The main classification splits into the sporadic and skeletal cases. The former is complete in all cardinalities. The latter is performed only in the countable case. The classification is considerably more complicated than for trees, and skeletal CFPOs exhibit rich, elaborate and rather surprising behavior. Features:  Lucid exposition of an important generalization of Droste's work
 Extended introduction clearly explaining the scope of the memoir
 Visually attractive topic with copious illustrations
 Selfcontained material, requiring few prerequisites
Readership Undergraduate students, graduate students, research mathematicians and physicists interested in elliptic functions. Table of Contents  Extended introduction
 Preliminaries
 Properties of \(k\)\(CS\)transitive CFPOs
 Constructing CFPOs
 Characterization and isomorphism theorems
 Classification of skeletal CFPOs (Part 1)
 Classification of skeletal CFPOs (Part 2)
 Sporadic cyclefree partial orders
