We present a combinatorial proof of Postnikov's hook length formula for binary trees. c 2007 Elsevier Ltd. All rights reserved. Let [n] = {1, 2, . . . , n}. It is well known ...
The Wiener index is analyzed for random recursive trees and random binary search trees in the uniform probabilistic models. We obtain the expectations, asymptotics for the varianc...
We divide a string into k segments, each with only one sort of symbols, so as to minimize the total number of exceptions. Motivations come from machine learning and data mining. F...