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IDEAL TRIANGLES IN EUCLIDEAN BUILDINGS AND BRANCHING TO LEVI SUBGROUPS
EUCLIDEAN BUILDINGS AND BRANCHING mathematics
2015/9/29
Let G denote a connected reductive group, de ned and split over Z, and
let M G denote a Levi subgroup. In this paper we study varieties of geodesic
triangles with xed vector-valued side-lengths ...
A Method for Obtaining Generating Function for Central Coefficients of Triangles
Obtaining Generating Function Central Coefficients of Triangles Combinatorics
2012/6/21
We consider problems of obtaining a generating function for the central coefficients of triangle $T(n,k)$, which is given by expression $[xG(x)]^k=\sum_{n\geqslant k} T(n,k)x^n$, $G(0)\neq 0$. We prov...
Areas of triangles and Beck's theorem in planes over finite fields
Areas of triangles Beck's theorem planes over finite fields Combinatorics
2012/5/9
It is shown that any subset $E$ of a plane over a finite field $\F_q$, of cardinality $|E|>q$ determines not less than $\frac{q-1}{2}$ distinct areas of triangles, moreover once can find such triangle...
Triangles on planar Jordan $C^1$-curves
Triangles planar Jordan $C^1$-curves Metric Geometry
2012/5/9
We prove that a Jordan $\calc^1$-curve in the plane contains any non-flat triangle up to translation and homothety with positive ratio. This is false if the curve is not $C^1$. The proof uses a bit co...
Invariant number triangles, eigentriangles and Somos-4 sequences
Invariant number triangles eigentriangles Somos-4 sequences Combinatorics
2011/9/22
Abstract: Using the language of Riordan arrays, we look at two related iterative processes on matrices and determine which matrices are invariant under these processes. In a special case, the invarian...
Triangles to Capture Social Cohesion
Triangles Capture Social Cohesion Social and Information Networks
2011/8/17
Abstract: Although community detection has drawn tremendous amount of attention across the sciences in the past decades, no formal consensus has been reached on the very nature of what qualifies a com...
Ehrhart's polynomial for equilateral triangles in $\mathbb Z^3$
Ehrhart polynomial linear Diophantine equations lattice points equilateral triangles sequences regular integral polytopes
2011/8/25
Abstract: In this paper we calculate the Ehrhart's polynomial associated with a 2-dimensional regular polytope (i.e. equilateral triangles) in $\mathbb Z^3$. The polynomial takes a relatively simple f...
A new family of elliptic curves with positive ranks arising from the Heron triangles
Elliptic curves Ranks Torsion group Heron’s Triangle
2011/2/28
The aim of this paper is to introduce a new family of elliptic curves with positive ranks.
Tuza conjectured that for every graph G, the maximum size of a set of edge-disjoint triangles and minimum size of a set of edges meeting all triangles, satisfy 2.
Degree conditions for the partition of a graph into triangles and quadrilaterals
degree partition triangle quadrilateral
2011/3/1
For two positive integers r and s with r ≥ 2s−2, if G is a graph of order 3r+4s such that d(x)+d(y) ≥ 4r+4s for every xy 6∈ E(G), then G independently contains r triangles and s quadrilaterals, ...
This is a study of the about structures in one-dimensional cellular automata, with the elementary cellular automaton Rule 54 as example. It uses the formalism of “flexible time” to derive expressions ...
A measure for the description of the chirality of triangles is introduced. The measure $X\delta$ is zero for triangles with at least one mirror axe, i.e. equilateral or isosceles triangles, and positi...
Let $E(k, \ell)$ denote the smallest integer such that any set of at least $E(k, \ell)$ points in the plane, no three on a line, contains either an empty convex polygon with $k$ vertices or an empty ...
Let be a random spherical triangle (meaning that vertices are independent and uniform on the unit sphere). A closed-form expression for the area density of has been known since 1867; a complicated...
Partitioning the triangles of the cross polytope into surfaces
cross polytope simplicial complexes triangulated surfaces difference cycles.
2010/12/6
We present a constructive proof, that there exists a decomposition of the 2-skeleton of the
k-dimensional cross polytope k into closed surfaces of genus ¤ 1, each with a transitive
automorphism gro...