{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IPJ55HXPD4YO554DUFEJC2HKU5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c68b3c15f8c8a7ec31ce335b2fd087a58d3318f61bd21cbfd08fb6a72054482e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-19T20:27:05Z","title_canon_sha256":"421cc0279bec57197bd8902d83632ee19f22a37b6b411e703a5417059d89911c"},"schema_version":"1.0","source":{"id":"1702.05791","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05791","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05791v1","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05791","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"pith_short_12","alias_value":"IPJ55HXPD4YO","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IPJ55HXPD4YO554D","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IPJ55HXP","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:cf0c1361ca2629f2ac71d6b596c7e53f76fe40a58e3c92402a58449489b8a07c","target":"graph","created_at":"2026-05-18T00:48:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we study positivity phenomena for the $e$-coefficients of Stanley's chromatic function of a graph. We introduce a new combinatorial object: the {\\em correct} sequences of unit interval orders, and using these, in certain cases, we succeed to construct combinatorial models of the coefficients appearing in Stanley's conjecture. Our main result is the proof of positivity of the coefficients $c_{n-k,1^k}$, $c_{n-2,2}$, $c_{n-3,2,1}$ and $c_{2^k,1^{n-2k}}$ of the expansion of the chromatic symmetric function in terms of the basis of the elementary symmetric polynomials for the case o","authors_text":"Alexander Paunov, Andr\\'as Szenes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-19T20:27:05Z","title":"A new approach to $e$-positivity for Stanley's chromatic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05791","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c2afb952b7f78e9ff7ccd6ccdc3d094a86f93eecea3efa4b6c3998c42fbf1d18","target":"record","created_at":"2026-05-18T00:48:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c68b3c15f8c8a7ec31ce335b2fd087a58d3318f61bd21cbfd08fb6a72054482e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-19T20:27:05Z","title_canon_sha256":"421cc0279bec57197bd8902d83632ee19f22a37b6b411e703a5417059d89911c"},"schema_version":"1.0","source":{"id":"1702.05791","kind":"arxiv","version":1}},"canonical_sha256":"43d3de9eef1f30eef783a1489168eaa74372307b3cd6a4dccac3c6ff071fd64c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43d3de9eef1f30eef783a1489168eaa74372307b3cd6a4dccac3c6ff071fd64c","first_computed_at":"2026-05-18T00:48:29.241303Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:29.241303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HXTln2ftcGpFZA9wSWWfy62g+S3474ueenCRJZPqxrv1OHBAPZ4FuY/2Frs6jl0GM2pOE/tznFLRXLOB54SZBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:29.242094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.05791","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2afb952b7f78e9ff7ccd6ccdc3d094a86f93eecea3efa4b6c3998c42fbf1d18","sha256:cf0c1361ca2629f2ac71d6b596c7e53f76fe40a58e3c92402a58449489b8a07c"],"state_sha256":"5d5ae49c1f6bbe51f9e966f5a6fbdb9212c959e871d40de92af50a9382635a27"}