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Launois \\cite{launois3} has shown that the generators consist of certain quantum minors of the matrix of canonical generators of $\\mathcal{O}_q(\\mathcal{M}_{m,n}(\\mathbb{K}))$ and in \\cite{launois2} gives an algorithm to find them. In this paper we modify a classic result of Lindstr\\\"{o}m \\cite{lind} and Gessel-Viennot~\\cite{gv} to show that a quantum minor is in the generating set for"},"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":"0907.1617","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-07-09T17:12:37Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"bc9a2c60baacbf9f97b38a69fcefa916b05690d4942e3f1a6f66d24e20637949","abstract_canon_sha256":"070ab1158fc2e76c7bd49946154b9f3e5dba24be13cad4433c030f01c839d4df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:57.373265Z","signature_b64":"uR4yaVf3uQtcjHt7PnbdBWk9n6s2QKsK0I5zJK+bkpBOeBDXXQAD1dUF7Sd0OazD8iQeqOzx1gmuaxn74VtmAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e315ae7f13993be5d878b4746d8927a8e3f8f7fec2653f2f00e2dd89653c49e5","last_reissued_at":"2026-05-18T04:40:57.372788Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:57.372788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Graph Theoretic Method for Determining Generating Sets of Prime Ideals in Quantum Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.QA","authors_text":"Karel Casteels","submitted_at":"2009-07-09T17:12:37Z","abstract_excerpt":"We take a graph theoretic approach to the problem of finding generators for those prime ideals of $\\mathcal{O}_q(\\mathcal{M}_{m,n}(\\mathbb{K}))$ which are invariant under the torus action ($\\mathbb{K}^*)^{m+n}$. 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