Immanant

In mathematics, the immanant of a matrix was defined by Dudley E. Littlewood and Archibald Read Richardson as a generalisation of the concepts of determinant and permanent.

Let ${\displaystyle \lambda =(\lambda _{1},\lambda _{2},\ldots )}$ be a partition of ${\displaystyle n}$ and let ${\displaystyle \chi _{\lambda }}$ be the corresponding irreducible representation-theoretic character of the symmetric group ${\displaystyle S_{n}}$. The immanant of an ${\displaystyle n\times n}$ matrix ${\displaystyle A=(a_{ij})}$ associated with the character ${\displaystyle \chi _{\lambda }}$ is defined as the expression

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