### Abstract

We prove the Pfaffian analog of the well-known diagonal expansion theorem for determinants. If P_{k} 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)=Σ_{1}^{N}P_{k}λ^{k}=Pfaffian [A(λ)] with a_{ij}(λ)=a_{ij}-(-1)^{j-i}λ^{2}. Our proof is an application of Wick's theorem.

Original language | English (US) |
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Pages (from-to) | 313-319 |

Number of pages | 7 |

Journal | Journal of Combinatorial Theory |

Volume | 5 |

Issue number | 3 |

DOIs | |

State | Published - Nov 1968 |

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## Cite this

Lieb, E. H. (1968). A theorem on Pfaffians.

*Journal of Combinatorial Theory*,*5*(3), 313-319. https://doi.org/10.1016/S0021-9800(68)80078-X