Combinatorial problems on trees: Partitions, δ-systems and large free subtrees
نویسندگان
چکیده
We prove partition theorems on trees and generalize to a setting of trees the theorems of Erdiis and Rado on A-systems and the theorems of Fodor and Hajnal on free sets. Let p be an infinite cardinal and TP be the tree of finite sequences of ordinals <p, with the partial ordering of being an initial segment. a Cb denotes that a is an initial segment of fi. A subtree of TP is a nonempty subset of T, closed under initial segments. T =S TP means that T is a subtree of TP and (T, 4) = TP. The following are extracts from Section 2, 3 and 4.
منابع مشابه
A Classification of Separable Rosenthal Compacta and Its Applications
Contents 1. Introduction 2 2. Ramsey properties of perfect sets and of subtrees of the Cantor tree 8 2.1. Notations 8 2.2. Partitions of trees 9 2.3. Partitions of perfect sets 11 3. Increasing and decreasing antichains of a regular dyadic tree 11 4. Canonicalizing sequential compactness of trees of functions 14 4.1. Sequential compactness of trees of functions 14 4.2. Equivalence of families o...
متن کاملLinked partitions and linked cycles
The notion of noncrossing linked partition arose from the study of certain transforms in free probability theory. It is known that the number of noncrossing linked partitions of [n+1] is equal to the n-th large Schröder number rn, which counts the number of Schröder paths. In this paper we give a bijective proof of this result. Then we introduce the structures of linked partitions and linked cy...
متن کاملNon-crossing Linked Partitions and Multiplication of Free Random Variables
The material gives a new combinatorial proof of the multiplicative property of the S-transform. In particular, several properties of the coefficients of its inverse are connected to non-crossing linked partitions and planar trees. AMS subject classification: 05A10 (Enumerative Combinatorics); 46L54(Free Probability and Free Operator Algebras).
متن کاملA general bijective algorithm for trees.
Trees are combinatorial structures that arise naturally in diverse applications. They occur in branching decision structures, taxonomy, computer languages, combinatiorial optimization, parsing of sentences, and cluster expansions of statistical mechanics. Intuitively, a tree is a collection of branches connected at nodes. Formally, it can be defined as a connected graph without cycles. Schroder...
متن کاملOrdered Construction of Combinatorial Objects
The generating function method for counting species of combinatorial objects is applied to the construction of the objects in order. The species considered are those described using context-free grammars with additional group-invariant operators. Some species constructible with this method are integer partitions, rooted trees of specified or unbounded degree including binary and ordered trees, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Ann. Pure Appl. Logic
دوره 33 شماره
صفحات -
تاریخ انتشار 1987