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Let G be a graph, and suppose each edge of G is independently deleted with fixed probability 0<=p<=1. Then the probability that no connected component of G is disconnected as ...

Let f(z) = z+a_1+a_2z^(-1)+a_3z^(-2)+... (1) = zsum_(n=0)^(infty)a_nz^(-n) (2) = zg(1/z) (3) be a Laurent polynomial with a_0=1. Then the Faber polynomial P_m(f) in f(z) of ...

A rook polynomial is a polynomial R_(m,n)(x)=sum_(k=0)^(min(m,n))r_kx^k (1) whose number of ways k nonattacking rooks can be arranged on an m×n chessboard. The rook ...

A polynomial given in terms of the Neumann polynomials O_n(x) by S_n(x)=(2xO_n(x)-2cos^2(1/2npi))/n.

A polynomial having random coefficients.

A Lucas polynomial sequence is a pair of generalized polynomials which generalize the Lucas sequence to polynomials is given by W_n^k(x) = ...

The approximating polynomial which has the smallest maximum deviation from the true function. It is closely approximated by the Chebyshev polynomials of the first kind.

The polynomial giving the number of colorings with m colors of a structure defined by a permutation group.

A polynomial with coefficients in a field is separable if its factors have distinct roots in some extension field.

The distance polynomial is the characteristic polynomial of the graph distance matrix. The following table summarizes distance polynomials for some common classes of graphs. ...