We define a new class of ordered sets, called free triangle orders. These are ordered sets represented by a left-to-right ordering on geometric objects contained in a horizontal strip in the plane. The objects are called “free triangles,” and have one vertex on each of the two boundaries of the strip and one vertex in its interior. These ordered sets generalize the classes of trapezoid and tria...

with considering a ‘triangle of three major currency pairs’, there is a tiny difference between multiplication of exchange rate for the first two currency pairs and the third. to discover whether this little difference can lead to a neutral arbitrage or not, i took portfolios of 35 baskets of three major currency pairs(combinations of all 7 major currencies). there are eight approaches (differe...

In his 1998 paper, Ryan classified the sets of unit, proper, and plain trapezoid and parallelogram orders. We extend this classification to include unit, proper, and plain triangle orders. We prove that there are 20 combinations of these properties that give rise to distinct classes of ordered sets, and order these classes by containment. Mathematics Subject Classifications (2000) 06A06, 05C62

We define the (n, i, f)-tube orders, which include interval orders, trapezoid orders, triangle orders, weak orders, order dimension n, and interval-orderdimension n as special cases. We investigate some basic properties of (n, i, f)-tube orders, and begin classifying them by containment.

The authors have previously shown [1] that to generate all trianglesaturated graphs (graphs of diameter at most 2), it suffices to begin with the primitive minimally triangle-saturated graphs. In the present paper two infinite families of primitive minimally triangle-saturated graphs are constructed: one family covers all odd orders n ≥ 3, the other all even orders n ≥ 4, and in each case all g...

Intersection graphs of geometric objects have been extensively studied, both due to their interesting structure and their numerous applications; prominent examples include interval graphs and permutation graphs. In this paper we study a natural graph class that generalizes both interval and permutation graphs, namely simple-triangle graphs. Simple-triangle graphs – also known as PI graphs (for ...

We propose a lossless, single-rate triangle mesh topology codec tailored for fast data-parallel GPU decompression. Our compression scheme coherently orders generalized triangle strips in memory. To unpack generalized triangle strips efficiently, we propose a novel parallel and scalable algorithm. We order vertices coherently to further improve our compression scheme. We use a variable bit-lengt...

A simple-triangle graph (also known as a PI graph) is the intersection graph of a family of triangles defined by a point on a horizontal line and an interval on another horizontal line. The recognition problem for simple-triangle graphs was a longstanding open problem, and recently a polynomial-time algorithm has been given [G. B. Mertzios, The Recognition of Simple-Triangle Graphs and of Linea...

We consider two types of Cheney–Sharma operators for functions defined on a triangle with all straight sides. construct their product and Boolean sum, we study interpolation properties the orders accuracy give different expressions corresponding remainders, highlighting symmetry between methods. also some illustrative numerical examples.