Stanley’s invariant theory survey

A survey of theory and methods of invariant item ordering.

In many testing situations, ordering the items by difficulty is helpful in analysing the testing data; examples include intelligence testing, analysis of differential item functioning, person-fit analysis, and exploring hypotheses about the order in which cognitive operations are acquired by children. In each situation, interpretation and analysis are made easier if the items are ordered by dif...

On Invariant Theory

Here we develop a technique of computing the invariants of n−ary forms and systems of forms using the discriminants of corresponding multilinear forms buit of their partial derivatives, which should be cosidered as generalizations of classical discriminants and resultants for binary forms. 0 Introduction Let f(y0, y1, ..., yn) = ∑ α1≤...≤αd cα1...αdyα1 ...yαd be an n + 1−ary form of degree d, w...

Arithmetic invariant theory

Basic geometric invariant theory

Adventures in Invariant Theory

We provide an introduction to enumerating and constructing invariants of group representations via character methods. The problem is con-textualised via two case studies, arising from our recent work: entan-glement invariants, for characterising the structure of state spaces for composite quantum systems; and Markov invariants, a robust alternative to parameter-estimation intensive methods of s...