An analog of the determinant for number triangles defined as a signed sum indexed by set partitions of into pairs of elements. The Pfaffian is the square root of the determinant of the corresponding antisymmetric matrix.

Bressoud, D. and Propp, J. "How the Alternating Sign Matrix Conjecture was Solved." Not. Amer. Math. Soc. 46, 637-646.

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Weisstein, Eric W. "Pfaffian." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Pfaffian.html