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On monotone functions of tree structures

Authors
Journal
Discrete Applied Mathematics
0166-218X
Publisher
Elsevier
Publication Date
Volume
5
Issue
2
Identifiers
DOI: 10.1016/0166-218x(83)90043-4

Abstract

Abstract Let T be a rooted tree structure with n nodes a 1,…, a n . A function f: { a 1,…, a n } into {1 < ⋯ < k} is called monotone if whenever a i is a son of a j , then f( a i ) ≥ f( a j ). The average number of monotone bijections is determined for several classes of tree structures. If k is fixed, for the average number of monotone functions asymptotic equivalents of the form c · ϱ − n n − 3 2 ( n → ∞) are obtained for several classes of tree structures.

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