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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"},"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":"1010.2606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-13T09:15:55Z","cross_cats_sorted":[],"title_canon_sha256":"49ec94a70b1bd05a69c853ff00e79ef4da48fbfa95f959e955882e017c079256","abstract_canon_sha256":"369f7fba6efbafdd5106338152d53c3f43baaf986435c95a6caaac43a0c48745"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:27.228971Z","signature_b64":"uF2mGoOwoz3LFtjtgLBRsylYWzWOLOfTL9/ilowDc2qWIeXewXW69RfL++jFi/pO11DC9aJZ/UrBeU18a9M0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb38d79c6971febde841010188f92c2cb3a74c294d040ebefac9c18d0bb2cbdd","last_reissued_at":"2026-05-18T04:39:27.228364Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:27.228364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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