20
votes
4answers
960 views

What are the applications of immanants?

Definitions of determinant: $det(A) = \sum_{\sigma \in S_n}(-1)^{\operatorname{sgn} \sigma}\prod_{i}a_{i, \sigma(i)}$ and permanent: $perm(A) = \sum_{\sigma \in S_n}\prod_{i}a_{i, \sigma(i)}$ ...
2
votes
0answers
249 views

Function recursion relation over symmetric group

Hi! Let P be a permutation in the symmetric group SN and let π=πj, j+1 be a transposition of elements j and j+1 of the permutation. Let A(P) be a function in dependence of the permutation P. ...
0
votes
1answer
495 views

Hankel determinants of symmetric functions

The starting point is that it is known that the Hankel determinants for the Catalan sequence give the number of nested sequences of Dyck paths. I would like to promote this to symmetric functions. ...
6
votes
3answers
1k views

Sarrus determinant rule: references, extensions

SEEKING REFERENCES FOR SARRUS' RULE AND EXTENSIONS An undergraduate came to me with an identity for 4x4 determinants that is actually correct: $\det(A)=h(A)+h(RA)+h(R^{2}A)$ where R cyclically ...