{"paper":{"title":"Injective split systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"G. E. Scholz, K. T. Huber, M. Hellmuth, P. F. Stadler, V. Moulton","submitted_at":"2022-11-08T15:43:57Z","abstract_excerpt":"A split system $\\mathcal S$ on a finite set $X$, $|X|\\ge3$, is a set of bipartitions or splits of $X$ which contains all splits of the form $\\{x,X-\\{x\\}\\}$, $x \\in X$. To any such split system $\\mathcal S$ we can associate the Buneman graph $\\mathcal B(\\mathcal S)$ which is essentially a median graph with leaf-set $X$ that displays the splits in $\\mathcal S$. In this paper, we consider properties of injective split systems, that is, split systems $\\mathcal S$ with the property that $\\mathrm{med}_{\\mathcal B(\\mathcal S)}(Y) \\neq \\mathrm{med}_{\\mathrm B(\\mathcal S)}(Y')$ for any 3-subsets $Y,Y'$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.04322","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.04322/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}