{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-minimum-value-of-the-colless-index","title":"The minimum value of the Colless index","arxiv_id":"1903.11670","date":"2019-07-23","proceeding":null,"authors":[],"abstract":"The Colless index is one of the oldest and most widely used balance indices\nfor rooted bifurcating trees. Despite its popularity, its minimum value on the\nspace $\\mathcal{T}_n$ of rooted bifurcating trees with $n$ leaves is only known\nwhen $n$ is a power of 2. In this paper we fill this gap in the literature, by\nproviding a formula that computes, for each $n$, the minimum Colless index on\n$\\mathcal{T}_n$, and characterizing those trees where this minimum value is\nreached.","url_abs":"http://arxiv.org/abs/1903.11670v4","url_pdf":"http://arxiv.org/pdf/1903.11670v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"the-minimum-value-of-the-colless-index","repo_url":"https://github.com/biocom-uib/Colless","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}