Brauer and partition diagram models for phylogenetic trees and forests.
Proc Math Phys Eng Sci
; 478(2262): 20220044, 2022 Jun.
Article
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| MEDLINE
| ID: mdl-35702594
ABSTRACT
We introduce a correspondence between phylogenetic trees and Brauer diagrams, inspired by links between binary trees and matchings described by Diaconis and Holmes (1998 Proc. Natl Acad. Sci. USA 95, 14 600-14 602. (doi10.1073/pnas.95.25.14600)). This correspondence gives rise to a range of semigroup structures on the set of phylogenetic trees, and opens the prospect of many applications. We furthermore extend the Diaconis-Holmes correspondence from binary trees to non-binary trees and to forests, showing for instance that the set of all forests is in bijection with the set of partitions of finite sets.
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2022
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Article