{"paper":{"title":"Double shortcuts of standard hypercube decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A conjecture on double shortcuts holds for standard hypercube decompositions of Bruhat intervals in the symmetric group.","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Margherita Zannoni","submitted_at":"2026-05-13T10:18:10Z","abstract_excerpt":"In this paper, we study the double shortcuts associated with pairs of standard hypercube decompositions of arbitrary Bruhat intervals in the symmetric group. Our results imply that a conjecture stated in [Bull. London Math. Soc., 57 (2025), no. 8] holds for the class of standard hypercube decompositions. If this conjecture were to hold for all hypercube decompositions, then the Combinatorial Invariance Conjecture for Kazhdan--Lusztig polynomials would follow."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our results imply that a conjecture stated in [Bull. London Math. Soc., 57 (2025), no. 8] holds for the class of standard hypercube decompositions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The results apply specifically to standard hypercube decompositions; the conjecture may fail or require different arguments for non-standard decompositions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The paper proves that a conjecture on double shortcuts holds for standard hypercube decompositions of Bruhat intervals, advancing the Combinatorial Invariance Conjecture for Kazhdan-Lusztig polynomials.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A conjecture on double shortcuts holds for standard hypercube decompositions of Bruhat intervals in the symmetric group.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"afd2f16881febc89da9205542f6b522af051797e4df31e4432b7e915e6346ed9"},"source":{"id":"2605.13304","kind":"arxiv","version":1},"verdict":{"id":"a7ebb87a-5679-4eba-8428-d55e7efb9126","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T20:22:36.328202Z","strongest_claim":"Our results imply that a conjecture stated in [Bull. London Math. Soc., 57 (2025), no. 8] holds for the class of standard hypercube decompositions.","one_line_summary":"The paper proves that a conjecture on double shortcuts holds for standard hypercube decompositions of Bruhat intervals, advancing the Combinatorial Invariance Conjecture for Kazhdan-Lusztig polynomials.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The results apply specifically to standard hypercube decompositions; the conjecture may fail or require different arguments for non-standard decompositions.","pith_extraction_headline":"A conjecture on double shortcuts holds for standard hypercube decompositions of Bruhat intervals in the symmetric group."},"references":{"count":17,"sample":[{"doi":"","year":2025,"title":"G.T. Barkley, C. Gaetz,Combinatorial invariance for elementary intervals, Math. Ann.392(2025), 3299–3317","work_id":"6febe6c5-42f4-4dcf-a031-21a2148e10e8","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"G.T. Barkley, C. Gaetz, T. Lam,Combinatorial invariance for the coefficient ofqin Kazhdan-Lusztig polynomials, arXiv:2601.07793 [math.CO]","work_id":"0314c597-1246-44ed-ab78-e32b3b41517a","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2005,"title":"A.Björner, F.Brenti,Combinatorics of Coxeter Groups, GraduateTextsinMathematics,231, Springer- Verlag, New York, 2005","work_id":"56750cf5-3f1f-4294-bea5-4b1ed333ab95","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"C. Blundell, L. Buesing, A. Davies, P. Veli˘ cković, G. Williamson,Towards combinatorial invariance for Kazhdan-Lusztig polynomials, Represent. Theory26(2022), 1145-1191","work_id":"392ba1e8-1979-4aa7-9f34-53d27ff60440","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1994,"title":"F.Brenti,A combinatorial formula for Kazhdan-Lusztig polynomials, Invent.Math.118(1994), 371-394","work_id":"b12079ec-3616-4e67-baaa-5d934816beb6","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":17,"snapshot_sha256":"6e3e22ccfaa012941e2c2d2423cba885eab1ea6f0b2ed36265a4f8288f98d1b7","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"}