In the recursive lamination of the disk, one tries to add chords one after another at random; a chord is kept and inserted if it does not intersect any of the previously inserted ones. Curien and Le Gall [Ann. Probab., vol. 39, pp. 2224–2270, 2011] have proved that the set of chords converges to a limit triangulation of the disk encoded by a continuous process M . Based on a new approach resemb...

1 PAIRS OF DUAL CONES Around 1900 Voronoï [10] formulated his fundamental algorithm to enumerate all similarity classes of perfect lattices in a given dimension. This algorithm has far reaching generalisations ([7], [6], [4]) used to compute generators and relators for arithmetic groups. A quite general situation, where one may apply Voronoï’s algorithm, is described in [7]: Let σ : V1 ×V2 → R ...

The pseudodeterminant pdet(M) of a square matrix is the last nonzero coefficient in its characteristic polynomial; for a nonsingular matrix, this is just the determinant. If ∂ is a symmetric or skewsymmetric matrix then pdet(∂∂t) = pdet(∂)2. Whenever ∂ is the kth boundary map of a self-dual CWcomplex X, this linear-algebraic identity implies that the torsion-weighted generating function for cel...

We say that a Hausdorff locale is compactly generated if it is the colimit of the diagram of its compact sublocales connected by inclusions. We show that this is the case if and only if the natural map of its frame of opens into the second Lawson dual is an isomorphism. More generally, for any Hausdorff locale, the second dual of the frame of opens gives the frame of opens of the colimit. In or...