منابع مشابه
On smallest triangles
Geoffrey Grimmett and Svante Janson Abstra t. Pick n points independently at random in R2 , according to a prescribed probability measure μ, and let ∆ 1 ≤ ∆ 2 ≤ . . . be the areas of the n 3 triangles thus formed, in non-decreasing order. If μ is absolutely continuous with respect to Lebesgue measure, then, under weak conditions, the set {n∆ i : i ≥ 1} converges as n → ∞ to a Poisson process wi...
متن کاملTiling Polygons with Lattice Triangles
Given a simple polygon with rational coordinates having one vertex at the origin and an adjacent vertex on the x-axis, we look at the problem of the location of the vertices for a tiling of the polygon using lattice triangles (i.e., triangles which are congruent to a triangle with the coordinates of the vertices being integer). We show that the coordinate of the vertices in any tiling are ratio...
متن کاملOn Ehrhart Polynomials of Lattice Triangles
The Ehrhart polynomial of a lattice polygon P is completely determined by the pair (b(P ), i(P )) where b(P ) equals the number of lattice points on the boundary and i(P ) equals the number of interior lattice points. All possible pairs (b(P ), i(P )) are completely described by a theorem due to Scott. In this note, we describe the shape of the set of pairs (b(T ), i(T )) for lattice triangles ...
متن کاملTrivial Meet and Join within the Lattice of Monotone Triangles
The lattice of monotone triangles (Mn,≤) ordered by entry-wise comparisons is studied. Let τmin denote the unique minimal element in this lattice, and τmax the unique maximum. The number of r-tuples of monotone triangles (τ1, . . . , τr) with minimal infimum τmin (maximal supremum τmax, resp.) is shown to asymptotically approach r|Mn| as n → ∞. Thus, with high probability this event implies tha...
متن کاملLattice Gravity and Random Surfaces
I review recent progress in simplicial quantum gravity in three and four dimensions, in particular new results on the phase structure of modified models of dynamical triangulations, the application of a strong-coupling expansion, and the benefits provided by including degenerate triangulations. In addition, I describe some recent numerical and analytical results on anisotropic crystalline membr...
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2016
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-016-0191-z