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The order distance can be useful in relational analyses because using<jats:bold>\u0394<\/jats:bold><jats:bold><jats:italic>(D)<\/jats:italic><\/jats:bold>instead of<jats:italic>D<\/jats:italic>may make such analyses less sensitive to small variations in<jats:bold><jats:italic>D<\/jats:italic><\/jats:bold>. Relatively little is known about properties of<jats:bold>\u0394<\/jats:bold><jats:bold><jats:italic>(D)<\/jats:italic><\/jats:bold>for general distances<jats:bold><jats:italic>D<\/jats:italic><\/jats:bold>. Indeed, nearly all previous work has focused on understanding the order distance of a<jats:italic>treelike distance<\/jats:italic>, that is, a distance that arises as the shortest path distances in a tree with non-negative edge weights and<jats:bold><jats:italic>X<\/jats:italic><\/jats:bold>mapped into its vertex set. In this paper we study the order distance<jats:bold>\u0394<\/jats:bold><jats:bold><jats:italic>(D)<\/jats:italic><\/jats:bold>for distances<jats:bold><jats:italic>D<\/jats:italic><\/jats:bold>that can be decomposed into sums of simpler distances called split-distances. Such distances<jats:bold><jats:italic>D<\/jats:italic><\/jats:bold>generalize treelike distances, and have applications in areas such as classification theory and phylogenetics.<\/jats:p>","DOI":"10.1007\/s11083-021-09579-y","type":"journal-article","created":{"date-parts":[[2021,9,20]],"date-time":"2021-09-20T20:37:20Z","timestamp":1632170240000},"page":"291-308","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Order Distances and Split Systems"],"prefix":"10.1007","volume":"39","author":[{"given":"Vincent","family":"Moulton","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5343-7236","authenticated-orcid":false,"given":"Andreas","family":"Spillner","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,9,20]]},"reference":[{"key":"9579_CR1","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198509424.001.0001","volume-title":"Phylogenetics","author":"C Semple","year":"2003","unstructured":"Semple, C., Steel, M.: Phylogenetics. 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