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Item Details
Title: THE STRUCTURE OF K-CS
TRANSITIVE CYCLE-FREE PARTIAL ORDERS
By: Richard Warren
Format: Paperback

List price: £53.95


We currently do not stock this item, please contact the publisher directly for further information.

ISBN 10: 082180622X
ISBN 13: 9780821806227
Publisher: AMERICAN MATHEMATICAL SOCIETY
Pub. date: 1 January, 1997
Series: Memoirs of the American Mathematical Society No. 614
Pages: 166
Description: Defines the class of cycle-free partial orders (CFPOs), and analyzes the CFPOs fulfilling a natural transitivity assumption, called $k$-connected set transitivity ($k$-$CS$-transitivity). This work generalizes Droste's classification of the countable $k$-transitive trees ($k \geq 2$).
Synopsis: In this work, the class of cycle-free 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. It's features include: 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; and, self-contained material, requiring few prerequisites.
Publication: US
Imprint: American Mathematical Society
Returns: Returnable
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