Counting canonical partitions in the random graph

Algorithms are given for computing the number of n-element diagonal sets and the number of n-element strongly diagonal sets of binary sequences of length at most 2n - 2. The first number corresponds to the number of weak embedding types of (2n - 1)-element transversal rooted binary set theoretic subtrees of binary sequences of length at most 2n-2. The second number corresponds to the number of parts, rn, in the canonical partition of Laflamme, Sauer and Vuksanovic of the n element subsets of an infinite random (Rado) graph, RG. The value rn is the critical value for a partition relation, since RG (RG)n </rn and RG (RG)n

• Type: Journal
• Year: 2008
• Where: COMBINATORICA
• Authors: Jean A. Larson
• Keywords: Binary Sequences, COMBINATORICA 2008, Diagonal Sets, N-element Diagonal Sets