{"paper":{"title":"The A-like matrices for a hypercube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Paul Terwilliger, Stefko Miklavic","submitted_at":"2010-10-13T09:15:55Z","abstract_excerpt":"Let $D$ denote a positive integer and let $Q_D$ denote the graph of the $D$-dimensional hypercube. Let $X$ denote the vertex set of $Q_D$ and let $A \\in \\MX$ denote the adjacency matrix of $Q_D$. A matrix $B \\in \\MX$ is called $A$-{\\em like} whenever both (i) $BA = AB$; (ii) for all $x,y \\in X$ that are not equal or adjacent, the $(x,y)$-entry of $B$ is zero. Let $\\Al$ denote the subspace of $\\MX$ consisting of the $A$-like elements. We decompose $\\Al$ into the direct sum of its symmetric part and antisymmetric part.  We give a basis for each part. The dimensions of the symmetric part and anti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2606","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":""},"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"}