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The cardinality of the Weyl alternation set associated to the highest root and zero weight of $\\mathfrak {sl}_{r+1}$ is given by the $r^{th}$ Fibonacci number. We then obtain the exponents of $\\mathfrak {sl}_{r+1}$ from this point of view."},"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":"1106.1408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-06-07T18:25:24Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ef1e9fed0b301d2758772401dfb27d501383f21a6e9d2223399195660b5aa0a3","abstract_canon_sha256":"f73c38dbabbba5f3ec8eee67b64c5443123ca01d1264fc150d9f15a318dff02e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:23.739866Z","signature_b64":"xgk4QoE9/1JKWDg39m3LfD2LkLXN7b6a24NR+E+h6EsxOnwaWtUbBHeFMeHYioDj0P/j6LiqspqmFx4Z1iAKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0cf11ae9011c15fbd49e3ea2fd2a5e57fc98ffe42dea6bdf3123f1b2bebcd4ab","last_reissued_at":"2026-05-18T04:20:23.739306Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:23.739306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the adjoint representation of $\\mathfrak{sl}_n$ and the Fibonacci numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Pamela E. 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