{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:E66Q5BN65APYNF2LBY3OH7HJDZ","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":"3f475137f024c5a131c8bb12148e715f1a5e22009206fd8f571efc519e616653","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-09T18:01:10Z","title_canon_sha256":"29466d563012da012e590c586f756f9020016fb15fb6924af66f9169c0d81531"},"schema_version":"1.0","source":{"id":"1307.2528","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2528","created_at":"2026-05-18T01:00:10Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2528v1","created_at":"2026-05-18T01:00:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2528","created_at":"2026-05-18T01:00:10Z"},{"alias_kind":"pith_short_12","alias_value":"E66Q5BN65APY","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"E66Q5BN65APYNF2L","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"E66Q5BN6","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:373d1196de509c46fd6e2d50d6f1c17cce9eb26faf224e6d4a9f7163d2f2dbda","target":"graph","created_at":"2026-05-18T01:00:10Z","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":"We explore monoids generated by operators on certain infinite partial orders. Our starting point is the work of Fomin and Greene on monoids satisfying the relations $(\\u{r}+\\u{r+1})\\u{r+1}\\u{r}=\\u{r+1}\\u{r}(\\u{r}+\\u{r+1})$ and $\\u{r}\\u{t}=\\u{s}\\u{r}$ if $|r-t|>1.$ Given such a monoid, the non-commutative functions in the variables $\\u{}$ are shown to commute. Symmetric functions in these operators often encode interesting structure constants. Our aim is to introduce similar results for more general monoids not satisfying the relations of Fomin and Greene. This paper is an extension of a talk b","authors_text":"Carolina Benedetti, Nantel Bergeron","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-09T18:01:10Z","title":"Fomin-Greene monoids and Pieri operations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2528","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:ce7308b76197ec23ac6a3f7ebaceebd9e8ca2e25bd37fb4b8052357c2a6f41a5","target":"record","created_at":"2026-05-18T01:00:10Z","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":"3f475137f024c5a131c8bb12148e715f1a5e22009206fd8f571efc519e616653","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-09T18:01:10Z","title_canon_sha256":"29466d563012da012e590c586f756f9020016fb15fb6924af66f9169c0d81531"},"schema_version":"1.0","source":{"id":"1307.2528","kind":"arxiv","version":1}},"canonical_sha256":"27bd0e85bee81f86974b0e36e3fce91e61dceee66e0ab021392c7974adcae629","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27bd0e85bee81f86974b0e36e3fce91e61dceee66e0ab021392c7974adcae629","first_computed_at":"2026-05-18T01:00:10.598256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:10.598256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FSRbqdR8XDnONXz1kTwKacTsj2N4+AoXr1Jl6zAWmtufCwZG8xShkkIhPyv27yi8Jp0TbgAxb2wlUx5qnogeCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:10.598920Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.2528","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce7308b76197ec23ac6a3f7ebaceebd9e8ca2e25bd37fb4b8052357c2a6f41a5","sha256:373d1196de509c46fd6e2d50d6f1c17cce9eb26faf224e6d4a9f7163d2f2dbda"],"state_sha256":"ab1eba901db14e2d8963d30259c1dc5386c2654eff797a3211b5eb9ed752304d"}