Applying a classical theorem of Smith, we show that the poset property of being Gorensteinâˆ— over Z2 is inherited by the subposet of fixed points under an involutive poset automorphism. As anâ€¦ (More)

We address the problem of computing the expected reversal distance of a genome with n genes obtained by applying t random reversals to the identity. A good approximation is the expected transpositionâ€¦ (More)

We prove the conjecture of A. Postnikov that (A) the number of regions in the inversion hyperplane arrangement associated with a permutation w âˆˆ Sn is at most the number of elements below w in theâ€¦ (More)

Given a simplicial hyperplane arrangement H and a subspace arrangement A embedded in H, we define a simplicial complex âˆ†A,H as the subdivision of the link of A induced by H. In particular, thisâ€¦ (More)

Natural Dowling analogues of the complex of phylogenetic trees are studied. Using discrete Morse theory, we find their homotopy types. In the process, the homotopy types of certain subposets ofâ€¦ (More)

Let W be a finite Coxeter group. For a given w âˆˆ W , the following assertion may or may not be satisfied: (âˆ—) The principal Bruhat order ideal of w contains as many elements as there are regions inâ€¦ (More)

Let G be a directed graph, and let âˆ†ACY G be the simplicial complex whose simplices are the edge sets of acyclic subgraphs of G. Similarly, we define âˆ†NSC G to be the simplicial complex with the edgeâ€¦ (More)

The open intervals in the Bruhat order on twisted involutions in a Coxeter group are shown to be PL spheres. This implies results conjectured by F. Incitti and sharpens the known fact that theseâ€¦ (More)

Given a Coxeter system (W, S) equipped with an involutive automorphism Î¸, the set of twisted identities is Î¹(Î¸) = {Î¸(w)w | w âˆˆ W}. We point out how Î¹(Î¸) shows up in several contexts and prove that ifâ€¦ (More)