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Eulerian poset
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<p>In <a href="/facts/Combinatorics/k14xUoKT">combinatorial</a> mathematics, an Eulerian poset is a <a href="/facts/Graded_poset/SAUdJ7op">graded poset</a> in which every nontrivial <a href="/facts/Partially_ordered_set/qb4a3FAX">interval</a> has the same number of elements of even rank as of odd rank. An Eulerian poset which is a <a href="/facts/Lattice_(order)/5ak6ufky">lattice</a> is an Eulerian lattice. These objects are named after <a href="/facts/Leonhard_Euler/z2fsbjgj">Leonhard Euler</a>. Eulerian lattices generalize <a href="/facts/Face_lattice/2pRHcRgC">face lattices</a> of <a href="/facts/Convex_polytope/2pRHcRgC">convex polytopes</a> and much recent research has been devoted to extending known results from <a href="/facts/Polyhedral_combinatorics/oVFESPjJ">polyhedral combinatorics</a>, such as various restrictions on <i>f</i>-vectors of convex <a href="/facts/Simplicial_polytope/TCJAMQth">simplicial polytopes</a>, to this more general setting. </p>