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Let s_k be the number of independent vertex sets of cardinality k in a graph G. The polynomial I(x)=sum_(k=0)^(alpha(G))s_kx^k, (1) where alpha(G) is the independence number, ...

A matrix whose entries are polynomials.

A polynomial having only real numbers as coefficients. A polynomial with real coefficients is a product of irreducible polynomials of first and second degrees.

Given a polynomial in a single complex variable with complex coefficients p(z)=a_nz^n+a_(n-1)z^(n-1)+...+a_0, the reciprocal polynomial is defined by ...

A polynomial is called unimodal if the sequence of its coefficients is unimodal. If P(x) is log-convex and Q(x) is unimodal, then P(x)Q(x) is unimodal.

A polynomial with real positive coefficients and roots which are either negative or pairwise conjugate with negative real parts.

A Laurent polynomial with coefficients in the field F is an algebraic object that is typically expressed in the form ...+a_(-n)t^(-n)+a_(-(n-1))t^(-(n-1))+... ...

A polynomial x^n+a_(n-1)x^(n-1)+...+a_1x+a_0 in which the coefficient of the highest order term is 1.

A homogeneous polynomial in two or more variables.

The ring R[x] of polynomials in a variable x.