A theorem on Pfaffians

Elliott H. Lieb

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


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 languageEnglish (US)
Pages (from-to)313-319
Number of pages7
JournalJournal of Combinatorial Theory
Issue number3
StatePublished - Nov 1968


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