{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:DTA6THZAMNRNO7ZU2RP6BMWDV3","short_pith_number":"pith:DTA6THZA","schema_version":"1.0","canonical_sha256":"1cc1e99f206362d77f34d45fe0b2c3aef337fef5dd9ab0dcc52471b1e88fa22d","source":{"kind":"arxiv","id":"1702.07859","version":1},"attestation_state":"computed","paper":{"title":"Zero sum partition into sets of the same order and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sylwia Cichacz","submitted_at":"2017-02-25T09:09:24Z","abstract_excerpt":"We will say that an Abelian group $\\Gamma$ of order $n$ has the $m$-\\emph{zero-sum-partition property} ($m$-\\textit{ZSP-property}) if $m$ divides $n$, $m\\geq 2$ and there is a partition of $\\Gamma$ into pairwise disjoint subsets $A_1, A_2,\\ldots , A_t$, such that $|A_i| = m$ and $\\sum_{a\\in A_i}a = g_0$ for $1 \\leq i \\leq t$, where $g_0$ is the identity element of $\\Gamma$.\n  In this paper we study the $m$-ZSP property of $\\Gamma$. We show that $\\Gamma$ has $m$-ZSP if and only if $|\\Gamma|$ is odd or $m\\geq 3$ and $\\Gamma$ has more than one involution. We will apply the results to the study of"},"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":"1702.07859","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-25T09:09:24Z","cross_cats_sorted":[],"title_canon_sha256":"5c8f52b49b0274d9035e602f01c574173d07c37d89d4945ceb2ee3fcd821deeb","abstract_canon_sha256":"c1998b4bbb5622fef0f8f5ec5e01da97a539b93178f2128a6e6b3f71eef45556"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:09.157708Z","signature_b64":"F2d6NXrBb0svbJUqZsFSRLsgi5W9EvVQgD1X2D/eZWuOySM5DsbzCdWFBx7WVQS6XvZJPeCdkGEcC5LlntL3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cc1e99f206362d77f34d45fe0b2c3aef337fef5dd9ab0dcc52471b1e88fa22d","last_reissued_at":"2026-05-18T00:23:09.157120Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:09.157120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Zero sum partition into sets of the same order and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sylwia Cichacz","submitted_at":"2017-02-25T09:09:24Z","abstract_excerpt":"We will say that an Abelian group $\\Gamma$ of order $n$ has the $m$-\\emph{zero-sum-partition property} ($m$-\\textit{ZSP-property}) if $m$ divides $n$, $m\\geq 2$ and there is a partition of $\\Gamma$ into pairwise disjoint subsets $A_1, A_2,\\ldots , A_t$, such that $|A_i| = m$ and $\\sum_{a\\in A_i}a = g_0$ for $1 \\leq i \\leq t$, where $g_0$ is the identity element of $\\Gamma$.\n  In this paper we study the $m$-ZSP property of $\\Gamma$. We show that $\\Gamma$ has $m$-ZSP if and only if $|\\Gamma|$ is odd or $m\\geq 3$ and $\\Gamma$ has more than one involution. We will apply the results to the study of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07859","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":"1702.07859","created_at":"2026-05-18T00:23:09.157242+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.07859v1","created_at":"2026-05-18T00:23:09.157242+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.07859","created_at":"2026-05-18T00:23:09.157242+00:00"},{"alias_kind":"pith_short_12","alias_value":"DTA6THZAMNRN","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"DTA6THZAMNRNO7ZU","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"DTA6THZA","created_at":"2026-05-18T12:31:12.930513+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/DTA6THZAMNRNO7ZU2RP6BMWDV3","json":"https://pith.science/pith/DTA6THZAMNRNO7ZU2RP6BMWDV3.json","graph_json":"https://pith.science/api/pith-number/DTA6THZAMNRNO7ZU2RP6BMWDV3/graph.json","events_json":"https://pith.science/api/pith-number/DTA6THZAMNRNO7ZU2RP6BMWDV3/events.json","paper":"https://pith.science/paper/DTA6THZA"},"agent_actions":{"view_html":"https://pith.science/pith/DTA6THZAMNRNO7ZU2RP6BMWDV3","download_json":"https://pith.science/pith/DTA6THZAMNRNO7ZU2RP6BMWDV3.json","view_paper":"https://pith.science/paper/DTA6THZA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.07859&json=true","fetch_graph":"https://pith.science/api/pith-number/DTA6THZAMNRNO7ZU2RP6BMWDV3/graph.json","fetch_events":"https://pith.science/api/pith-number/DTA6THZAMNRNO7ZU2RP6BMWDV3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DTA6THZAMNRNO7ZU2RP6BMWDV3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DTA6THZAMNRNO7ZU2RP6BMWDV3/action/storage_attestation","attest_author":"https://pith.science/pith/DTA6THZAMNRNO7ZU2RP6BMWDV3/action/author_attestation","sign_citation":"https://pith.science/pith/DTA6THZAMNRNO7ZU2RP6BMWDV3/action/citation_signature","submit_replication":"https://pith.science/pith/DTA6THZAMNRNO7ZU2RP6BMWDV3/action/replication_record"}},"created_at":"2026-05-18T00:23:09.157242+00:00","updated_at":"2026-05-18T00:23:09.157242+00:00"}