Foata-Fuchs对Cayley公式的证明，以及它的概率应用

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Electronic Communications in Probability Pub Date : 2021-07-20 DOI:10.1214/23-ecp523

L. Addario-Berry, Serte Donderwinkel, M. Maazoun, James Martin

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引用次数: 3

摘要

由Foata和Fuchs（1970）给出了Cayley公式的一个非常简单的双射证明。当通过概率透镜观察时，这种双射是非常有用的；我们解释了它可以用来推导具有给定度的随机树（包括随机d元树）的概率恒等式、边界和生长过程的一些方法。我们还引入了有根树度序列上的一个偏序，并推测它在给定度的随机有根树的高度上诱导了一个随机偏序。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Foata–Fuchs proof of Cayley’s formula, and its probabilistic uses

We present a very simple bijective proof of Cayley's formula due to Foata and Fuchs (1970). This bijection turns out to be very useful when seen through a probabilistic lens; we explain some of the ways in which it can be used to derive probabilistic identities, bounds, and growth procedures for random trees with given degrees, including random d-ary trees. We also introduce a partial order on the degree sequences of rooted trees, and conjecture that it induces a stochastic partial order on heights of random rooted trees with given degrees.

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来源期刊

Electronic Communications in Probability 工程技术-统计学与概率论

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Electronic Communications in Probability (ECP) publishes short research articles in probability theory. Its sister journal, the Electronic Journal of Probability (EJP), publishes full-length articles in probability theory. Short papers, those less than 12 pages, should be submitted to ECP first. EJP and ECP share the same editorial board, but with different Editors in Chief.