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In combinatorial mathematics, an Eulerian poset is a graded poset in which every nontrivial interval has the same number of elements of even rank as of odd rank. An Eulerian poset which is a lattice is an Eulerian lattice. These objects are named after Leonhard Euler. Eulerian lattices generalize face lattices of convex polytopes and much recent research has been devoted to extending known results from polyhedral combinatorics, such as various restrictions on ''f''-vectors of convex simplicial polytopes, to this more general setting. == Examples == * The face lattice of a convex polytope, consisting of its faces, together with the smallest element, the empty face, and the largest element, the polytope itself, is an Eulerian lattice. The odd–even condition follows from Euler's formula. * Any simplicial generalized homology sphere is an Eulerian lattice. * Let ''L'' be a regular cell complex such that |''L''| is a manifold with the same Euler characteristic as the sphere of the same dimension (this condition is vacuous if the dimension is odd). Then the poset of cells of ''L'', ordered by the inclusion of their closures, is Eulerian. * Let ''W'' be a Coxeter group with Bruhat order. Then (''W'',≤) is an Eulerian poset. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Eulerian poset」の詳細全文を読む スポンサード リンク
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