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Alon, Moran and Yehudayoff showed that $$n^{(1+o(1))\\frac{1}{k+1}\\binom{n}{k}}\\leq m(n,k)\\leq n^{(1+o(1))\\binom{n}{k}}.$$ We close the gap by showing that $\\log \\left(m(n,k)\\right)= {(1+o(1))\\binom{n}{k}}\\log n$ and show how a tight asymptotic for the logarithm of the number of induced matchings between two adjacent small layers of $Q_n$ follows as a corollary.\n  Next, we consider the integrity $I(Q_n)$ of the hypercub"},"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":"1710.08509","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-23T21:20:09Z","cross_cats_sorted":[],"title_canon_sha256":"46565641fccce0bacb7bf4694250313a3328690fb5fa1ced60a8278a7563f92e","abstract_canon_sha256":"8e03090bfaf8cb28912a478e6393e7922e451569ff76df0401c4dbc63c2837e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:15.848524Z","signature_b64":"WJtttDz2rN2yMbYUeyuzPmP/YhHSMb+4Tio6g8VnzSZQRXwhgzMBnlr4QvNOxv31bjmGFnrNp7tS0lngh4shAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbda9f5c8bcef1f901a40f4e6140924691d67b9ceb07ad53dbd91e15aa92276b","last_reissued_at":"2026-05-18T00:32:15.847907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:15.847907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two results about the hypercube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adam Zsolt Wagner, Jozsef Balogh, Tamas Meszaros","submitted_at":"2017-10-23T21:20:09Z","abstract_excerpt":"First we consider families in the hypercube $Q_n$ with bounded VC dimension. 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