The Enumeration of Rooted Trees by Total Height
نویسنده
چکیده
The height (as in [3] and [4]) of a point in a rooted tree is the length of the path (that is, the number of lines in the path) from it to the root; the total height of a rooted tree is the sum of the heights of its points. The latter arises naturally in studies of random neural networks made by one of us (N.J.A.S.), where the enumeration of greatest interest is that of trees with all points distinctly labeled. Wiite J vh for the number of rooted trees with p labeled points and total height h, and
منابع مشابه
Building Random Trees from Blocks
Many modern networks grow from blocks. We study the probabilistic behavior of parameters of a blocks tree, which models several kinds of networks. It grows from building blocks that are themselves rooted trees. We investigate the number of leaves, depth of nodes, total path length, and height of such trees. We use methods from the theory of Pólya urns and martingales.
متن کاملMining Frequent Rooted Trees and Free Trees Using Canonical Forms
Tree structures are used extensively in domains such as computational biology, pattern recognition, XML databases, computer networks, and so on. In this paper, we present HybridTreeMiner, a computationally efficient algorithm that discovers all frequently occurring subtrees in a database of rooted unordered trees. The algorithm mines frequent subtrees by traversing an enumeration tree that syst...
متن کاملCMTreeMiner: Mining Both Closed and Maximal Frequent Subtrees
Tree structures are used extensively in domains such as computational biology, pattern recognition, XML databases, computer networks, and so on. One important problem in mining databases of trees is to find frequently occurring subtrees. However, because of the combinatorial explosion, the number of frequent subtrees usually grows exponentially with the size of the subtrees. In this paper, we p...
متن کاملInfinite Systems of Functional Equations and Gaussian Limiting Distributions
Systems of functional equations for generating functions appear in many combinatorial enumeration problems, for example in tree enumeration problems or in the enumeration of planar graphs (and related problems), see Drmota (2009). Usually, these enumeration techniques can be extended to take several parameters into account: the number of vertices, the number of edges, the number of vertices of ...
متن کاملRestricted rooted non-separable planar maps
Tutte founded the theory of enumeration of planar maps in a series of papers in the 1960s. Rooted non-separable planar maps have connections, for example, to pattern-avoiding permutations, and they are in one-to-one correspondence with the β(1, 0)-trees introduced by Cori, Jacquard and Schaeffer in 1997. In this paper we enumerate 2-face-free rooted non-separable planar maps and obtain restrict...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008