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Let $$\\|f\\|_A := \\sup_{x \\in A}{|f(x)|}$$ for real-valued functions $f$ defined on a set $A \\subset {\\Bbb R}$. Let $$V_a^b(f) := \\int_a^b{|f^{\\prime}(x)| \\, dx}$$ denote the total variation of a continuously differentiable function $f$ on an interval $[a,b]$. We prove that there are absolute constants $c_1 > 0$ and $c_2 > 0$ such that $$c_1 \\frac nk\\leq \\min_{P \\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1809.07733","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CA","submitted_at":"2018-09-20T16:50:46Z","cross_cats_sorted":[],"title_canon_sha256":"4139ba590fbdd881a1774ae959744e6a8b03928a7e49131a3968f8ce57393b95","abstract_canon_sha256":"09b5ab0591b5f6576dd5f78dea58e328a34b34e9729cc46278c47cbb8e594fea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:15.309425Z","signature_b64":"hxoAGq1guewvybXqR4+yTFeVK7W+hjfVI5rGCVy5ehA9r3pJAfGHORC4/iXyRALqodEgY5dDU8IpWiHCh4WwDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1828cf9a4f18d60369b2cc087e63f860d1dbb21276cb8b0f5a7fd4a219f10629","last_reissued_at":"2026-05-18T00:05:15.308906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:15.308906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reverse Markov- and Bernstein-type inequalities for incomplete polynomials","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Tam\\'as Erd\\'elyi","submitted_at":"2018-09-20T16:50:46Z","abstract_excerpt":"Let ${\\mathcal P}_k$ denote the set of all algebraic polynomials of degree at most $k$ with real coefficients. Let ${\\mathcal P}_{n,k}$ be the set of all algebraic polynomials of degree at most $n+k$ having exactly $n+1$ zeros at $0$. Let $$\\|f\\|_A := \\sup_{x \\in A}{|f(x)|}$$ for real-valued functions $f$ defined on a set $A \\subset {\\Bbb R}$. Let $$V_a^b(f) := \\int_a^b{|f^{\\prime}(x)| \\, dx}$$ denote the total variation of a continuously differentiable function $f$ on an interval $[a,b]$. We prove that there are absolute constants $c_1 > 0$ and $c_2 > 0$ such that $$c_1 \\frac nk\\leq \\min_{P \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07733","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1809.07733","created_at":"2026-05-18T00:05:15.308982+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.07733v1","created_at":"2026-05-18T00:05:15.308982+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07733","created_at":"2026-05-18T00:05:15.308982+00:00"},{"alias_kind":"pith_short_12","alias_value":"DAUM7GSPDDLA","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"DAUM7GSPDDLAG2NS","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"DAUM7GSP","created_at":"2026-05-18T12:32:19.392346+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DAUM7GSPDDLAG2NSZQEH4Y7YMD","json":"https://pith.science/pith/DAUM7GSPDDLAG2NSZQEH4Y7YMD.json","graph_json":"https://pith.science/api/pith-number/DAUM7GSPDDLAG2NSZQEH4Y7YMD/graph.json","events_json":"https://pith.science/api/pith-number/DAUM7GSPDDLAG2NSZQEH4Y7YMD/events.json","paper":"https://pith.science/paper/DAUM7GSP"},"agent_actions":{"view_html":"https://pith.science/pith/DAUM7GSPDDLAG2NSZQEH4Y7YMD","download_json":"https://pith.science/pith/DAUM7GSPDDLAG2NSZQEH4Y7YMD.json","view_paper":"https://pith.science/paper/DAUM7GSP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.07733&json=true","fetch_graph":"https://pith.science/api/pith-number/DAUM7GSPDDLAG2NSZQEH4Y7YMD/graph.json","fetch_events":"https://pith.science/api/pith-number/DAUM7GSPDDLAG2NSZQEH4Y7YMD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DAUM7GSPDDLAG2NSZQEH4Y7YMD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DAUM7GSPDDLAG2NSZQEH4Y7YMD/action/storage_attestation","attest_author":"https://pith.science/pith/DAUM7GSPDDLAG2NSZQEH4Y7YMD/action/author_attestation","sign_citation":"https://pith.science/pith/DAUM7GSPDDLAG2NSZQEH4Y7YMD/action/citation_signature","submit_replication":"https://pith.science/pith/DAUM7GSPDDLAG2NSZQEH4Y7YMD/action/replication_record"}},"created_at":"2026-05-18T00:05:15.308982+00:00","updated_at":"2026-05-18T00:05:15.308982+00:00"}