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Bruhat interval polytopes were studied recently by Kodama and the second author, in the context of the Toda lattice and the moment map on the flag variety.\n  In this paper we study combinatorial aspects of Bruhat interval polytopes. For example, we give an inequality des"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1406.5202","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-19T20:11:03Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"dca25927625ac68a9df14ee02ee545f5fa7701317eb72691fbff2a01f380103b","abstract_canon_sha256":"30d8b539e479ebf9e63f178709910fddd03a051a58c097b943870f17102bb223"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:33.832123Z","signature_b64":"S8N7fTU35KDLRWP/lMxAejsLPuq0Ni0EZ0/dnfAu++QjTgg2ZQlMbSN2fyV0J82ZraNCvgc2IkrieJjPX9JWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"048b4c6262b159f1507329220b1928068b91832009f351917d50c01563113c7f","last_reissued_at":"2026-05-18T01:55:33.831560Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:33.831560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bruhat Interval Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Emmanuel Tsukerman, Lauren Williams","submitted_at":"2014-06-19T20:11:03Z","abstract_excerpt":"Let u and v be permutations on n letters, with u <= v in Bruhat order. 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