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The flip graphs of a quadrilateral (top-left), a pentagon (top-right), and a hexagon (bottom). Examples of flips in dimension 1 (top-right), 2 (top-left and central row), and 3 (bottom row). In mathematics, a flip graph is a graph whose vertices are combinatorial or geometric objects, and whose edges link two of these objects when they can be ...
The flip distance between two triangulations is the minimum number of flips needed to transform one triangulation into another. [1] It can also be described as the shortest path distance in a flip graph , a graph that has a vertex for each triangulation and an edge for each flip between two triangulations. [ 1 ]
In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle .
Wiley-Interscience series in discrete mathematics and optimization. Vol. 54. Wiley-IEEE. ISBN 978-0-471-32710-3. Pemmaraju, Sriram V.; Skiena, Steven S. (2003). "Permutations and combinations". Computational discrete mathematics: combinatorics and graph theory with Mathematica. Cambridge University Press. ISBN 978-0-521-80686-2.
If the relative canonical ring is finitely generated (as an algebra over ) then the morphism + is called the flip of if is relatively ample, and the flop of if K is relatively trivial. (Sometimes the induced birational morphism from X {\displaystyle X} to X + {\displaystyle X^{+}} is called a flip or flop.)
In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.
Image source: The Motley Fool. Prologis (NYSE: PLD) Q4 2024 Earnings Call Jan 21, 2025, 12:00 p.m. ET. Contents: Prepared Remarks. Questions and Answers. Call ...
The transpose of a matrix A, denoted by A T, [3] ⊤ A, A ⊤, , [4] [5] A′, [6] A tr, t A or A t, may be constructed by any one of the following methods: . Reflect A over its main diagonal (which runs from top-left to bottom-right) to obtain A T
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