{"paper":{"title":"Fomin-Greene monoids and Pieri operations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carolina Benedetti, Nantel Bergeron","submitted_at":"2013-07-09T18:01:10Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2528","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"}