We prove the Pfaffian analog of the well-known diagonal expansion theorem for determinants. If Pk is the sum of the Pfaffians of all the k-square principal triangular subarrays of a given N-square triangular array A then P(λ)=Σ1NPkλk=Pfaffian [A(λ)] with aij(λ)=aij-(-1)j-iλ2. Our proof is an application of Wick's theorem.
|Original language||English (US)|
|Number of pages||7|
|Journal||Journal of Combinatorial Theory|
|State||Published - Nov 1968|