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The theorem, originally conjectured by Berge (1960, 1961), that a graph is perfect iff neither the graph nor its graph complement contains an odd graph cycle of length at ...

A symmetric polynomial on n variables x_1, ..., x_n (also called a totally symmetric polynomial) is a function that is unchanged by any permutation of its variables. In other ...

Transfinite induction, like regular induction, is used to show a property P(n) holds for all numbers n. The essential difference is that regular induction is restricted to ...

Let c_k be the number of vertex covers of a graph G of size k. Then the vertex cover polynomial Psi_G(x) is defined by Psi_G(x)=sum_(k=0)^(|G|)c_kx^k, (1) where |G| is the ...

Let Xi be the xi-function defined by Xi(iz)=1/2(z^2-1/4)pi^(-z/2-1/4)Gamma(1/2z+1/4)zeta(z+1/2). (1) Xi(z/2)/8 can be viewed as the Fourier transform of the signal ...

An antisymmetric matrix, also known as a skew-symmetric or antimetric matrix, is a square matrix that satisfies the identity A=-A^(T) (1) where A^(T) is the matrix transpose. ...

An Argand diagram is a plot of complex numbers as points z=x+iy in the complex plane using the x-axis as the real axis and y-axis as the imaginary axis. In the plot above, ...

A black bishop graph is a graph formed from possible moves of a bishop chess piece, which may make diagonal moves of any length on a chessboard (or any other board), when ...

A box integral for dimension n with parameters q and s is defined as the expectation of distance from a fixed point q of a point r chosen at random over the unit n-cube, ...

Various forms of opening and closing bracket-like delimiters are used for a number of distinct notational purposes in mathematics. The most common variants of bracket ...