论文信息 - Counting canonical partitions in the random graph

Counting canonical partitions in the random graph

Joyce trees have concrete realizations as J-trees of sequences of 0’s and 1’s. Algorithms are given for computing the number of minimal height J-trees of d-ary sequences with n leaves and the number of them with minimal parent passing numbers to obtain polynomials ρn(d) for the full collection and αn(d) for the subcollection.The number of traditional Joyce trees is the tangent number αn(1); αn(2) is the number of cells in the canonical partition by Laflamme, Sauer and Vuksanovic of n-element subsets of the infinite random (Rado) graph; and ρn(2) is the number of weak embedding types of rooted n-leaf J-trees of sequences of 0’s and 1’s.

Jean A. Larson

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