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A306422
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Maximal number of coalescent histories among matching pairs of binary, rooted leaf-labeled gene trees and species trees with n leaves.
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0
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OFFSET
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1,3
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COMMENTS
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Consider the unlabeled binary, rooted, leaf-labeled tree topologies with n leaves (A001190). For each unlabeled topology, choose an arbitrary labeling with distinct labels for the n leaves, and assign it to both gene tree and species tree. Compute the number of coalescent histories for that matching (gene tree, species tree) pair according to a recursion (Rosenberg 2007, Theorem 3.1). The sequence a(n) gives the largest number observed among all unlabeled topologies.
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LINKS
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CROSSREFS
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A000108 and A005817 give the numbers of coalescent histories for specific families of matching gene trees and species trees.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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