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Fixed points of involutive automorphisms of the Bruhat order
Abstract Applying a classical theorem of Smith, we show that the poset property of being Gorenstein * over Z 2 is inherited by the subposet of fixed points under an involutive poset automorphism. AsExpand
  • 41
  • 10
  • Open Access
Twisted identities in Coxeter groups
Abstract Given a Coxeter system (W,S) equipped with an involutive automorphism θ, the set of twisted identities is $$\iota (\theta )=\{\theta(w^{-1})w\mid w\in W\}.$$ We point out how ι(θ) shows upExpand
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  • Open Access
The combinatorics of twisted involutions in Coxeter groups
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 theseExpand
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  • 6
  • Open Access
Link complexes of subspace arrangements
  • Axel Hultman
  • Mathematics, Computer Science
  • Eur. J. Comb.
  • 15 July 2005
Given a simplicial hyperplane arrangement H and a subspace arrangement A embedded in H, we define a simplicial complex @D"A","H as the subdivision of the link of A induced by H. In particular, thisExpand
  • 15
  • 4
  • Open Access
From Bruhat intervals to intersection lattices and a conjecture of Postnikov
We prove the conjecture of A. Postnikov that (A) the number of regions in the inversion hyperplane arrangement associated with a permutation w@?S"n is at most the number of elements below w in theExpand
  • 15
  • 4
  • Open Access
Inversion arrangements and Bruhat intervals
  • Axel Hultman
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. A
  • 4 October 2010
Let W be a finite Coxeter group. For a given w@?W, the following assertion may or may not be satisfied:(@?)The principal Bruhat order ideal of w contains as many elements as there are regions in theExpand
  • 7
  • 3
  • Open Access
Estimating the expected reversal distance after a fixed number of reversals
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 transpositionExpand
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  • Open Access
Criteria for rational smoothness of some symmetric orbit closures
Abstract Let G be a connected reductive linear algebraic group over C with an involution θ. Denote by K the subgroup of fixed points. In certain cases, the K-orbits in the flag variety G / B areExpand
  • 11
  • 2
  • Open Access
The topology of spaces of phylogenetic trees with symmetry
  • Axel Hultman
  • Computer Science, Mathematics
  • Discret. Math.
  • 1 June 2007
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 ofExpand
  • 7
  • 1
Directed Subgraph Complexes
  • Axel Hultman
  • Mathematics, Computer Science
  • Electron. J. Comb.
  • 26 October 2004
Let $G$ be a directed graph, and let $\Delta^{ACY}_G$ be the simplicial complex whose simplices are the edge sets of acyclic subgraphs of $G$. Similarly, we define $\Delta^{NSC}_G$ to be theExpand
  • 6
  • 1