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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,...

This question was originally asked in (https://math.stackexchange.com/questions/4265063/computation-of-the-pfaffian-of-a-particular-matrix). I did not find any satisfactory answer there. So I am ...

It is known (see for instance Beauville - Determinantal hypersurfaces) that a generic homogeneous polynomial in $5$ variables of degree $5$ with complex coefficients can be written as the Pfaffian of ...