Flags and Shellings of Eulerian Cubical Posets

Abstract. A cubical analog of Stanley's theorem expressing the cd-index of an Eulerian simplicial poset in terms of its h-vector is presented. This result implies that the cd-index conjecture for Gorenstein* cubical posets follows from Ron Adin's conjecture on the non-negativity of his cubical h-vector for Cohen-Macaulay cubical posets. For cubical spheres, the standard definition of shelling is shown to be equivalent to the spherical one. A cubical analog of Stanley's conjecture about the connection between the cd-index of semisuspended simplicial shelling components and the reduced variation polynomials of certain subclasses of André permutations is established. The notion of signed André permutations used in this result is a common generalization of two earlier definitions of signed André permutations.

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