{"paper":{"title":"Fuzzy latin squares and balanced permutation pattern statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Joy Cooper, Peter J. Dukes","submitted_at":"2026-08-05T18:50:09Z","abstract_excerpt":"A latin square of order $n$ can be viewed as a partition of the $n \\times n$ all-ones matrix into permutation matrix summands. Here, we consider a relaxation in which the matrix summands are allowed to be induced from shorter permutations. For $\\sigma \\in S_k$, the `fuzzy permutation matrix' $P_\\sigma^{\\uparrow n}$ arises from combining all $\\binom{n}{k}^2$ order-preserving embeddings of the $k \\times k$ permutation matrix $P_\\sigma$ into an $n \\times n$ matrix. We define a fuzzy latin square as a linear combination of $n \\times n$ fuzzy permutation matrices $P_\\sigma^{\\uparrow n}$ equaling a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05335","kind":"arxiv","version":1},"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/2608.05335/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"}