{"paper":{"title":"Some Instances of Homomesy Among Ideals of Posets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shahrzad Haddadan","submitted_at":"2014-10-17T18:46:16Z","abstract_excerpt":"Given a permutation $\\tau$ defined on a set of combinatorial objects $S$, together with some statistic $f:S\\rightarrow \\mathbb{R}$, we say that the triple $\\langle S, \\tau,f \\rangle$ exhibits homomesy if $f$ has the same average along all orbits of $\\tau$ in $S$. This phenomenon was noticed by Panyushev (2007) and later studied, named and extended by Propp and Roby (2013). After Propp and Roby's paper, homomesy has received a lot of attention and a number of mathematicians are intrigued by it. While seeming ubiquitous, homomesy is often surprisingly non-trivial to prove. Propp and Roby studied"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4819","kind":"arxiv","version":3},"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"}