{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ARMEOQVBTRTX5KBZKJNZBWGX7U","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":"18e7b68e89e62833b56e3d82b04497690d41bbac6577cf77dadda70b9a33b52f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-13T17:48:38Z","title_canon_sha256":"f496835a86ea324869f503f407ad96df930952c9daf6af7a8cdd1d1c5e02f4d7"},"schema_version":"1.0","source":{"id":"1906.05848","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.05848","created_at":"2026-05-17T23:43:24Z"},{"alias_kind":"arxiv_version","alias_value":"1906.05848v1","created_at":"2026-05-17T23:43:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.05848","created_at":"2026-05-17T23:43:24Z"},{"alias_kind":"pith_short_12","alias_value":"ARMEOQVBTRTX","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"ARMEOQVBTRTX5KBZ","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"ARMEOQVB","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:5af7bca5db8a18ad98a575c115d69ba7ab718f8bd93fa9fd4c8f215228fabdb2","target":"graph","created_at":"2026-05-17T23:43:24Z","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":"Using the notion of Mahonian statistic on acyclic posets, we introduce a $q$-analogue of the $h$-polynomial of a simple generalized permutohedron. We focus primarily on the case of nestohedra and on explicit computations for many interesting examples, such as $S_n$-invariant nestohedra, graph associahedra, and Stanley--Pitman polytopes. For the usual (Stasheff) associahedron, our generalization yields an alternative $q$-analogue to the well-studied Narayana numbers.","authors_text":"Eric Katz, McCabe Olsen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-13T17:48:38Z","title":"Multivariate polynomials for generalized permutohedra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05848","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:a4521bfecc7af19fca967acaacad9e3f78087d5ab97afd1981b6ea2dcc970c77","target":"record","created_at":"2026-05-17T23:43:24Z","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":"18e7b68e89e62833b56e3d82b04497690d41bbac6577cf77dadda70b9a33b52f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-13T17:48:38Z","title_canon_sha256":"f496835a86ea324869f503f407ad96df930952c9daf6af7a8cdd1d1c5e02f4d7"},"schema_version":"1.0","source":{"id":"1906.05848","kind":"arxiv","version":1}},"canonical_sha256":"04584742a19c677ea839525b90d8d7fd2cff90b41769872360500313d5899265","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04584742a19c677ea839525b90d8d7fd2cff90b41769872360500313d5899265","first_computed_at":"2026-05-17T23:43:24.269738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:24.269738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NvB30k/gAsTf3+zVRRTHqHWGM9RxgHlCArNWThmpqpWM9+pQdZUns7uhmGV/X+tAzfLTLeaPIy94U/lxJZ1DAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:24.270444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.05848","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4521bfecc7af19fca967acaacad9e3f78087d5ab97afd1981b6ea2dcc970c77","sha256:5af7bca5db8a18ad98a575c115d69ba7ab718f8bd93fa9fd4c8f215228fabdb2"],"state_sha256":"11c85d9562aafae69656cc9b86090a5d6c8ef63e2ff6d0e9342fd1969939646a"}