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Fixed points of involutive automorphisms of the Bruhat order

- Axel Hultman
- Mathematics
- 4 March 2004

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. As… Expand

Twisted identities in Coxeter groups

- Axel Hultman
- Mathematics
- 7 February 2007

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 up… Expand

The combinatorics of twisted involutions in Coxeter groups

- Axel Hultman
- Mathematics
- 19 November 2004

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 these… Expand

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, this… Expand

From Bruhat intervals to intersection lattices and a conjecture of Postnikov

- Axel Hultman, Svante Linusson, John Shareshian, Jonas Sjöstrand
- Mathematics, Computer Science
- J. Comb. Theory, Ser. A
- 5 October 2007

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 the… Expand

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 the… Expand

Estimating the expected reversal distance after a fixed number of reversals

- N. Eriksen, Axel Hultman
- Computer Science, Mathematics
- Adv. Appl. Math.
- 1 April 2004

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 transposition… Expand

Criteria for rational smoothness of some symmetric orbit closures

- Axel Hultman
- Mathematics
- 6 July 2009

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 are… Expand

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 of… Expand

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 the… Expand