On the enumeration of rooted trees with fixed size of maximal decreasing trees

초록

Let T(n) be the set of rooted labeled trees on (0, ..., n). A maximal decreasing subtree of a rooted labeled tree is defined by the maximal subtree from the root with all edges being decreasing. In this paper, we study a new refinement T(n.k) of T(n), which is the set of rooted labeled trees whose maximal decreasing subtree has k + 1 vertices. (C) 2011 Elsevier B.V. All rights reserved.

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