{"paper":{"title":"Heaps and Two Exponential Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Emma Yu Jin","submitted_at":"2014-07-01T13:55:38Z","abstract_excerpt":"Take ${\\sf Q}=({\\sf Q}_1,{\\sf Q}_2,\\ldots)$ to be an exponential structure and $M(n)$ to be the number of minimal elements of ${\\sf Q}_n$ where $M(0)=1$. Then a sequence of numbers $\\{r_n({\\sf Q}_n)\\}_{n\\ge 1}$ is defined by the equation \\begin{eqnarray*} \\sum_{n\\ge 1}r_n({\\sf Q}_n)\\frac{z^n}{n!\\,M(n)}=-\\log(\\sum_{n\\ge 0}(-1)^n\\frac{z^n}{n!\\,M(n)}). \\end{eqnarray*} Let $\\bar{{\\sf Q}}_n$ denote the poset ${\\sf Q}_n$ with a $\\hat{0}$ adjoined and let $\\hat{1}$ denote the unique maximal element in the poset ${\\sf Q}_n$. Furthermore, let $\\mu_{{\\sf Q}_n}$ be the M\\\"{o}bius function on the poset $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0242","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"}