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The Computer Journal 1989 32(1):76-85; doi:10.1093/comjnl/32.1.76
© 1989 by British Computer Society
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Classes of Admissible Permutations that are Generatable by Depth-first Traversals of Ordered Trees

M. C. Er *

Department of Computer Science, The University of Western Australia, Nedlands, WA 6009, Australia

Admissible permutations may be characterised by the absence of certain subsequences in permutations, and may also be characterised by combinations of depth-first traversals of ordered trees. Out of 36 possible combinations, it is shown that there are four essential non-degenerated classes of admissible permutations. The relations between these four classes are established using the inverse, the reverse and the complement mappings. Consequently, any class of admissible permutations can be derived from another class using these mappings. Furthermore, some orderings of admissible permutations are related to the orderings of ordered trees and their binary representations. Such relationships enable any types of the above combinatorial objects to be generated systematically in some orders.

Received March 1986. revised June 1987.

* Department of Computer Science, The University of Western Australia, Nedlands, WA 6009, Australia


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