{"paper":{"title":"Nilpotent matrices having a given Jordan type as maximum commuting nilpotent orbit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.RT"],"primary_cat":"math.RA","authors_text":"Anthony Iarrobino, Bart Van Steirteghem, Leila Khatami, Rui Zhao","submitted_at":"2014-09-08T02:51:54Z","abstract_excerpt":"The Jordan type of a nilpotent matrix is the partition giving the sizes of its Jordan blocks. We study pairs of partitions $(P,Q)$, where $Q={\\mathcal Q}(P)$ is the Jordan type of a generic nilpotent matrix A commuting with a nilpotent matrix B of Jordan type $ P$. T. Ko\\v{s}ir and P. Oblak have shown that $Q$ has parts that differ pairwise by at least two. Such partitions, which are also known as \"super distinct\" or \"Rogers-Ramanujan\", are exactly those that are stable or \"self-large\" in the sense that ${\\mathcal Q}(Q)=Q$.\n  In 2012 P. Oblak formulated a conjecture concerning the cardinality "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2192","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","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"}