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We obtain new algorithms for the following two problems first studied by Koutis and Williams \\cite{Kou08, Wi09, KW16}. k-MLC: Compute the sum of the coefficients of all degree-$k$ multilinear monomials in the polynomial $f$. k-MMD: Test if there is a nonzero degree-$k$ multilinear monomial in the polynomial $f$.\n  Our algorithms are based on the fact that the Hada"},"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":"1807.04496","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2018-07-12T09:34:29Z","cross_cats_sorted":[],"title_canon_sha256":"b0f267e77a89ac8b26a3f13969d806a1391b2f7908863f2e23d79393d92a3391","abstract_canon_sha256":"6d05a22bcf7c9bc0a8e228406d885b48750f379b6b8c51bdec83ab76b56e5e29"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:07:10.102032Z","signature_b64":"E/kvaJwUtn10II3Lels6fC9/Eq7w/XwA42uA1etARflkBZN/cCGfOlpQ/Twm9TwHa2E/EVR6Tfug+dYP0NVxAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0714ed7d7bcb24450f8a0e62fd2ac51862f48c7eee4491c639ae802c48e8533b","last_reissued_at":"2026-07-05T01:07:10.101559Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:07:10.101559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fast Exact Algorithms Using Hadamard Product of Polynomials","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Abhranil Chatterjee, Partha Mukhopadhyay, Rajit Datta, V.Arvind","submitted_at":"2018-07-12T09:34:29Z","abstract_excerpt":"Let $C$ be an arithmetic circuit of $poly(n)$ size given as input that computes a polynomial $f\\in\\mathbb{F}[X]$, where $X=\\{x_1,x_2,\\ldots,x_n\\}$ and $\\mathbb{F}$ is any field where the field arithmetic can be performed efficiently. We obtain new algorithms for the following two problems first studied by Koutis and Williams \\cite{Kou08, Wi09, KW16}. k-MLC: Compute the sum of the coefficients of all degree-$k$ multilinear monomials in the polynomial $f$. k-MMD: Test if there is a nonzero degree-$k$ multilinear monomial in the polynomial $f$.\n  Our algorithms are based on the fact that the Hada"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04496","kind":"arxiv","version":2},"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/1807.04496/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1807.04496","created_at":"2026-07-05T01:07:10.101629+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.04496v2","created_at":"2026-07-05T01:07:10.101629+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.04496","created_at":"2026-07-05T01:07:10.101629+00:00"},{"alias_kind":"pith_short_12","alias_value":"A4KO27L3ZMSE","created_at":"2026-07-05T01:07:10.101629+00:00"},{"alias_kind":"pith_short_16","alias_value":"A4KO27L3ZMSEKD4K","created_at":"2026-07-05T01:07:10.101629+00:00"},{"alias_kind":"pith_short_8","alias_value":"A4KO27L3","created_at":"2026-07-05T01:07:10.101629+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.08347","citing_title":"On Explicit Branching Programs for the Rectangular Determinant and Permanent Polynomials","ref_index":2018,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/A4KO27L3ZMSEKD4KBZRP2KWFDB","json":"https://pith.science/pith/A4KO27L3ZMSEKD4KBZRP2KWFDB.json","graph_json":"https://pith.science/api/pith-number/A4KO27L3ZMSEKD4KBZRP2KWFDB/graph.json","events_json":"https://pith.science/api/pith-number/A4KO27L3ZMSEKD4KBZRP2KWFDB/events.json","paper":"https://pith.science/paper/A4KO27L3"},"agent_actions":{"view_html":"https://pith.science/pith/A4KO27L3ZMSEKD4KBZRP2KWFDB","download_json":"https://pith.science/pith/A4KO27L3ZMSEKD4KBZRP2KWFDB.json","view_paper":"https://pith.science/paper/A4KO27L3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.04496&json=true","fetch_graph":"https://pith.science/api/pith-number/A4KO27L3ZMSEKD4KBZRP2KWFDB/graph.json","fetch_events":"https://pith.science/api/pith-number/A4KO27L3ZMSEKD4KBZRP2KWFDB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A4KO27L3ZMSEKD4KBZRP2KWFDB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A4KO27L3ZMSEKD4KBZRP2KWFDB/action/storage_attestation","attest_author":"https://pith.science/pith/A4KO27L3ZMSEKD4KBZRP2KWFDB/action/author_attestation","sign_citation":"https://pith.science/pith/A4KO27L3ZMSEKD4KBZRP2KWFDB/action/citation_signature","submit_replication":"https://pith.science/pith/A4KO27L3ZMSEKD4KBZRP2KWFDB/action/replication_record"}},"created_at":"2026-07-05T01:07:10.101629+00:00","updated_at":"2026-07-05T01:07:10.101629+00:00"}