{"paper":{"title":"Diagonally Embedded Sets of ${\\rm Trop}^+G(2,n)$'s in ${\\rm Trop}\\, G(2,n)$: Is There a Critical Value of $n$?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.CO","authors_text":"Freddy Cachazo","submitted_at":"2021-04-21T16:40:30Z","abstract_excerpt":"The tropical Grassmannian ${\\rm Trop}\\, G(2,n)$ is known to be the moduli space of unrooted metric trees with $n$ leaves. A positive part can be defined for each of the $(n-1)!/2$ possible planar orderings, $\\alpha$, and agrees with the corresponding planar trees in the moduli space, ${\\rm Trop}^{\\alpha}G(2,n)$. Motivated by a physical application we study the way ${\\rm Trop}^{\\alpha}G(2,n)$ and ${\\rm Trop}^{\\beta}G(2,n)$ intersect in ${\\rm Trop}\\, G(2,n)$. We define their intersection number as the number of unrooted binary trees that belong to both and construct a $(n-1)!/2\\times (n-1)!/2$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.10628","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/2104.10628/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"}