{"paper":{"title":"Counting Borel Orbits in Symmetric Varieties of Types $BI$ and $CII$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.CO","authors_text":"Mahir Bilen Can, \\\"Ozlem U\\u{g}urlu","submitted_at":"2018-01-17T01:54:15Z","abstract_excerpt":"This is a continuation of our combinatorial program on the enumeration of Borel orbits in symmetric varieties of classical types. Here, we determine the generating series the numbers of Borel orbits in $\\mathbf{SO}_{2n+1}/\\mathbf{S(O}_{2p}\\times \\mathbf{O}_{2q+1}\\mathbf{)}$ (type $BI$) and in $\\mathbf{Sp}_n/\\mathbf{Sp}_p\\times \\mathbf{Sp}_q$ (type $CII$). In addition, we explore relations to lattice path enumeration."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05524","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":""},"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"}