{"paper":{"title":"Frozen-corner enumeration of Alternating Sign Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.CO","authors_text":"Andrei G. Pronko, Filippo Colomo","submitted_at":"2025-09-17T14:16:06Z","abstract_excerpt":"An Alternating Sign Matrix (ASM) is a square matrix with entries in $\\{0,1,-1\\}$, and such that: $i)$ in each row and columns, nonzero entries alternate in sign; $ii)$ for any given row or column, entries sum up to $1$. We define the frozen-square enumeration as the enumeration of $n\\times n$ ASMs under the refinement of having, located in a corner, an $s\\times s$ square of entries that are all zeroes. We state a conjectural formula for such enumeration, in terms of the determinant of some $s\\times s$ matrix whose entries are given explicitly. We provide numerical support in favour of our conj"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.14006","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.14006/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}