Volume of Hypercubes Clipped by Hyperplanes and Combinatorial Identities
نویسندگان
چکیده
There was an elegant expression for the volume of hypercube [0, 1] clipped by a hyperplane. We generalize the formula to the case of more than one hyperplane. Furthermore we derive several combinatorial identities from the volume expressions of clipped hypercubes.
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خواص متریک و ترکیبیاتی مکعبهای فیبوناتچی و لوکاس
An n-dimensional hypercube, Q_n, is a graph in which vertices are binary strings of length n where two vertices are adjacent if they differ in exactly one coordinate. Hypercubes and their subgraphs have a lot of applications in different fields of science, specially in computer science. This is the reason why they have been investigated by many authors during the years. Some of their subgraphs ...
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