Counting canonical partitions in the random graph |
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Authors: | Jean A Larson |
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Institution: | (1) Department of Mathematics, University of Florida, P.O. Box, Gainesville, Florida 118105, USA |
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Abstract: | 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 ρ
n
(d) for the full collection and α
n
(d) for the subcollection.
The number of traditional Joyce trees is the tangent number α
n
(1); α
n
(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 ρ
n
(2) is the number of weak embedding types of rooted n-leaf J-trees of sequences of 0’s and 1’s.
The author thanks the University of Tel Aviv for hospitality in April 2004 when much of this work was done. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 05A15 05C05 03E02 05C80 |
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