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Order polynomial
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<p>The order polynomial is a <a href="/facts/Polynomial/Lzak8VVx">polynomial</a> studied in mathematics, in particular in <a href="/facts/Algebraic_graph_theory/5HNDPx8g">algebraic graph theory</a> and <a href="/facts/Algebraic_combinatorics/9b47n3Fh">algebraic combinatorics</a>. The order polynomial counts the number of <a href="/facts/Order-preserving_map/MjQK0YL2">order-preserving maps</a> from a <a href="/facts/Partially_ordered_set/qb4a3FAX">poset</a> to a <a href="/facts/Total_order/xnTtmuYJ">chain</a> of length n {\displaystyle n} . These order-preserving maps were first introduced by <a href="/facts/Richard_P._Stanley/8bQ4QrLM">Richard P. Stanley</a> while studying ordered structures and partitions as a Ph.D. student at <a href="/facts/Harvard_University/Lhy9L1cx">Harvard University</a> in 1971 under the guidance of <a href="/facts/Gian-Carlo_Rota/zLSPLVwR">Gian-Carlo Rota</a>. </p>