Odd or even on plane trees

Sen Peng Eu*, Shu Chung Liu, Yeong Nan Yeh

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

7 引文 斯高帕斯(Scopus)

摘要

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 finding a direct two-to-one correspondence for this property. In this article, we give three different 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.

原文英語
頁(從 - 到)189-196
頁數8
期刊Discrete Mathematics
281
發行號1-3
DOIs
出版狀態已發佈 - 2004 四月 28

ASJC Scopus subject areas

  • 理論電腦科學
  • 離散數學和組合

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