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The Casoratian of sequences x_n^((1)), x_n^((2)), ..., x_n^((k)) is defined by the k×k determinant C(x_n^((1)),x_n^((2)),...,x_n^((k))) =|x_n^((1)) x_n^((2)) ... x_n^((k)); ...

A chiral knot is a knot which is not capable of being continuously deformed into its own mirror image. A knot that can be so deformed is then called an amphichiral knot. ...

An alternative term for a binomial coefficient, in which (n; k) is read as "n choose k." R. K. Guy suggested this pronunciation around 1950, when the notations ^nC_r and ...

Given a series of the form A(z)=sum_(k)a_kz^k, the notation [z^k](A(z)) is used to indicate the coefficient a_k (Sedgewick and Flajolet 1996). This corresponds to the Wolfram ...

Two elements x and y of a set S are said to be commutative under a binary operation * if they satisfy x*y=y*x. (1) Real numbers are commutative under addition x+y=y+x (2) and ...

The graph corresponding to the complete k-ary tree on n nodes is implemented in the Wolfram Language as KaryTree[n, k].

The concatenation of two strings a and b is the string ab formed by joining a and b. Thus the concatenation of the strings "book" and "case" is the string "bookcase". The ...

Since the derivative of a constant is zero, any constant may be added to an indefinite integral (i.e., antiderivative) and will still correspond to the same integral. Another ...

Attractive compounds can be constructed from the cube 3-compounds and their octahedron 3-compound duals. One is illustrated above. This compound will be implemented in a ...

The cube-octahedron 5-compound is a polyhedron compound of the cube 5-compound and its dual, the octahedron 5-compound. It will be implemented in a future version of the ...