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Title: A Bijective Proof of Complete Binary Trees
Authors: 施耀振
Contributors: 李陽明
Date: 1990
Issue Date: 2016-05-03 14:17:31 (UTC+8)
Abstract: 在此,將介紹一個從Tnc 映至Sn的bijection, 其中Tnc = {tc: tc 是一有2n-1 個點的complete binary tree ,其中有一點被圈選} & Sn={x: x是一有n個黑點,n-1個白點的string }。並藉此求得k1*k 2*... *kn在” *”不可結合( nonassociative )之下的二元運算( binary operation )方法數。這個解與Catalan number 一致。
Reference: [1] J. A. Bondy & U. S. R. Murty, Graph Theory With Application. London. Macmillan, 1976.
[2] Gary Chartrant & Linda Lesniak. Graphs & Digraphs. 2nd ed ., Wadsworth Inc., Belmont. 1986.
[3] Marshall Hall. JR., Combinatorial Theory, 2nd ed., New York, Wiley. 1986.
[4] Richard Johnsonbaugh, Discrete Mathematics, New York,Macmillan; London. Collier Macmillan. 1984.
[5] I. Niven. Formal Power Series, Amer. Math. Monthly 76 (1969), pp.871-889.
[6] Dennis Staton & Dennis White, Constructive Combinatorics. New York. Springer-Verlag, 1986, p.60.
[7] Alan Tucker. Applied Combinatorics, New York, Wiley, 1980.
[8] "Introduction to the Theory of Combinatorial Species", 由中央研究院數學研究所 葉永南 先生提供.
Description: 碩士
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Data Type: thesis
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