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In this case, the associated Kazhdan-Lusztig-Vogan polynomials $P_{v,u}$ can be indexed by pairs of fixed point free involutions $v\\geq u$, where $\\geq$ denotes the Bruhat order on $S_{2n}$. We prove that these polynomials are combinatorial invariants in the sense that if $f: [u, w_0 ] \\rightarrow [u , w_0]$ is a poset isomorphism of upper intervals in the Bruhat order on fixed point free involutions, then $P_{v,u} = P_{f(v),u}"},"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":"1612.07133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-21T14:23:23Z","cross_cats_sorted":[],"title_canon_sha256":"2da5a7caf63410fb78915ecbd262e522edf2e130902c4b7ffe652c141bb0dbc4","abstract_canon_sha256":"1fed650d3d37b12b05de9587a1b46a466a4ad642e272ab72f99e327290ddcd26"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:14.601877Z","signature_b64":"5X2rJKzhk0bf3sUTUOPQjx+dzKduLq4PU6Ld3Ay12IlKUZyLtupvNzMlJ4tfOSCf90Q9QCJxgcLxy55zd7+6Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"162c226dbcee9ff156d06bf252b9b790bf6e41850a05ecb5e3c8447498bcc752","last_reissued_at":"2026-05-18T00:54:14.601423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:14.601423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorial Invariance of Kazhdan-Lusztig-Vogan Polyomials for Fixed Point Free Involutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Axel Hultman, Nancy Abdallah","submitted_at":"2016-12-21T14:23:23Z","abstract_excerpt":"When $Sp(2n,\\mathbb{C})$ acts on the flag variety of $SL(2n,\\mathbb{C})$, the orbits are in bijection with fixed point free involutions in the symmetric group $S_{2n}$. 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