A generating function for X-forests
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The Tuffley poset is a poset of a certain kind of semi-labelled forests called X-forests, where X is a finite set of labels. This poset is closely related to a topological space of phylogenetic trees called the edgeproduct space. A generating function of the elements in the Tuffley poset with respect to natural statistics is studied and a closed formula is found. In addition, a closed formula for the corresponding generating function of X-trees is found. Singularity analysis is used on these formulas to find asymptotics for the number of components, edges, and unlabelled nodes in X-forests and X-trees as |X| → ∞.
IdentifiersURN: urn:nbn:se:liu:diva-100892OAI: oai:DiVA.org:liu-100892DiVA: diva2:664196