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.
Pfaffian
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References
Bressoud, D. and Propp, J. "How the Alternating Sign Matrix Conjecture was Solved." Not. Amer. Math. Soc. 46, 637-646.Referenced on Wolfram|Alpha
PfaffianCite this as:
Weisstein, Eric W. "Pfaffian." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Pfaffian.html