Odd or even on plane trees
نویسندگان
چکیده
Over all plane trees with n edges, the total number of vertices with odd degree is twice the number of those with odd outdegree. Deutsch and Shapiro posed the problem of 3nding a direct two-to-one correspondence for this property. In this article, we give three di5erent proofs via generating functions, an inductive proof and a two-to-one correspondence. Besides, we introduce two new sequences which enumerate plane trees according to the parity of the number of leaves. The explicit formulae for these sequences are given. As an application, the relation provides a simple proof for a problem concerning colored nets in Stanley’s Catalan Addendum. c © 2003 Elsevier B.V. All rights reserved.
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عنوان ژورنال:
- Discrete Mathematics
دوره 281 شماره
صفحات -
تاریخ انتشار 2004