In mathematical invariant theory

Invariant theory

Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties from the point of view of their effect on functions...

, the catalecticant of a binary form

Invariant of a binary form

In mathematical invariant theory, an invariant of a binary form is a polynomial in the coefficients of a binary form in two variables x and y that remains invariant under unimodular transformations of the variables x and y.-Terminology:...

 of degree 2n is a polynomial in its coefficients that vanishes when the binary form is a sum of at most n powers . It was introduced by ; see . The word catalectic

Catalectic

A catalectic line is a metrically incomplete line of verse, lacking a syllable at the end or ending with an incomplete foot. One form of catalexis is headlessness, where the unstressed syllable is dropped from the beginning of the line....

 refers to an incomplete line of verse, lacking a syllable at the end or ending with an incomplete foot.

The catalecticant can be given as the determinant of a catalecticant matrix , also called a Hankel matrix, that is a square matrix with constant (positive sloping) skew-diagonals, such as