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4 votes
0 answers
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Combinatorial interpretation of a pfaffian identity?

Let $n$ be a positive even integer. We introduce three types of skew-symmetric matrices, $A_{n+2}$, $B_n$ and $C_n$ (the subscript denotes the dimension of the matrices) in terms of the variables $z_1,...
12 votes
1 answer
741 views

Determinant is to Pfaffian as resultant is to what?

This is an irresponsible question: I do not have done any thinking on it, or even literature search. I just became curious whether there is some modification of the notion of a common root of two ...
4 votes
3 answers
1k views

Detecting if a polynomial is a Pfaffian

Given an explicit polynomial, is there any kind of trick/algorithm to check whether it is a pfaffian of a matrix with linear entries? The pfaffian can be defined as $\sqrt{{\rm det}(A) } $ when $A$ ...