Recently it has been noticed that many interesting combinatorial objects belong to a class of semigroups called left regular bands, and that random walks on these semigroups encode several well-knownâ€¦ (More)

These pages serve two purposes. First, they are notes to accompany the talk Hyperbolic and projective geometry in constraint programming for CAD by Walter Whiteley at the JÃ¡nos Bolyai Conference onâ€¦ (More)

Using a result of T. P. Bidigare [Bidigare, 1997], we identity the descent algebra Î£k(W ) (over a field k) of a finite Coxeter group W with a subalgebra of kF , an algebra built from the hyperplaneâ€¦ (More)

This article presents a study of an algebra spanned by the faces of a hyperplane arrangement. The quiver with relations of the algebra is computed and the algebra is shown to be a Koszul algebra. Itâ€¦ (More)

We define Markoff words as certain factors appearing in bi-infinite words satisfying the Markoff condition. We prove that these words coincide with central words, yielding a new characterization ofâ€¦ (More)

Recently it has been noticed that many interesting combinatorial objects belong to a class of semigroups called left regular bands, and that random walks on these semigroups encode several well-knownâ€¦ (More)

Hyperplane arrangements and descent algebras Franco V Saliola saliola-DesAlgLectureNotes.pdf version of 10 January 2006 Errata and addenda by Darij Grinberg I will refer to the results appearing inâ€¦ (More)

This article presents a study of an algebra spanned by the faces of a hyperplane arrangement. The quiver with relations of the algebra is computed and the algebra is shown to be a Koszul algebra. Itâ€¦ (More)