A. Renyi and G. Szekeres, On the height of trees, J. Austral. Math. Soc. 7 (1967), 497--507.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....elements of an integral, non decreasing function. They, too, are not suitable for the general DCMST problem. There is a significant amount of literature on the height and diameter of a random tree. The expected height of a random labeled rooted tree is (2 p n) as derived by Rnyi and Szekeres [18]. The problem of tree enumeration by height and diameter, for labeled and unlabeled trees, was addressed by Riordan [19] among others [12] Szekeres [20] showed that n 342171 . 3 and n 20151315 . 3 is the expected value of diameter and the diameter of maximum probability, respectively, for a ....

Rnyi, A., Szekeres, G., "On the height of trees," Journal of the Australian Mathematical Society, 7 (1967), pp. 497-507.

....normalized stack size of a ( tries T be de ned as s(T ) s(T ) p for = Then we obviously nd that the r th moment of the normalized stack size is asymptotically given by r(r 1) r 2 (r) in the limit. Those are exactly the r th moments of the theta distribution [17] whose cummulative distribution function is H(x) 4x 3 5 2 X k 0 k 2 exp( k 2 2 =x 2 ) with the corresponding density h(x) 4x X k 1 k 2 (2k 2 x 2 3) exp( k 2 x 2 ) 7) Therefore we can conclude: Corollary 2 The normalized stack size of ( tries s(T ) ....

A. Renyi and G. Szekeres, On the height of trees, Austral. J. Math. 7, 1967, 497-507.

....are even easier to obtain, since they only involve upper bounds for the b h (z) b h 1 (z) inside the disk of convergence z 1 4. Xi In addition to the methods of [132, 133, 126] that were mentioned above, there are also other techniques for studying heights of trees, such as those of [60, 331]. However, there are problems about obtaining fully rigorous proofs that way. See the remarks in [126] on this topic. Most of these methods can be extended to study related problems, such as those of diameters of trees [357] The results of Example 15.3 can be extended to other families of trees ....

A. Renyi and G. Szekeres, On the height of trees, J. Austral. Math. Soc., 7 (1967), pp. 497--507.

....the trees. In many cases what is needed, though, is information about the distribution of heights among trees of a given size, so that we need to hold the size fixed and vary the height. The first results of this kind which involved nonlinear analytic iteration were obtained by Renyi and Szekeres [34] in a study of rooted nonplanar labeled trees. By means of an extensive study (which relied heavily on [36] of the sequence of functions G 0 (z) G 1 (z) where G 0 (z) z and G h 1 (z) z exp(G h (z) h 0 , 3.1) they showed that the average height of rooted nonplanar labeled ....

A. Renyi and G. Szekeres, On the height of trees, Australian J. of Math., 7 (1967), 497-507.

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A. Renyi and G. Szekeres, On the height of trees, J. Austral. Math. Soc. 7 (1967), 497--507.

No context found.

A. Renyi and G. Szekeres, On the height of trees, J. Austral. Math. Soc. 7 (1967), 497-507.

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A. Renyi and G. Szekeres, On the height of trees, J. Austral. Math. Soc. 7 (1967) 497---507; MR0219440 (36 #2522).

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A. Renyi & G. Szekeres, (1967) On the height of trees. J. Aust. Math. Soc. 7, 497-507.

No context found.

A. Renyi & G. Szekeres, (1967) On the height of trees. J. Aust. Math. Soc. 7, 497-507.

No context found.

A. Renyi & G. Szekeres, (1967) On the height of trees. J. Aust. Math. Soc. 7, 497-507.

No context found.

A. R'enyi and G. Szekeres, On the height of trees, J. Austral. Math. Soc., 7 (1967), pp. 497--507.

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