Bourbaki

Example

Tag 0DLA, permanent. Cite it as [Bourbaki, Tag 0DLA].

Algebra, chapter IX, § 5. Propriétés spéciales aux formes bilinéaires alternées

Suppose:

α12=−α21=β1,α34=−α43=β2,…,α2m−1,2m=−α2m,2m−1=βm,\alpha_{12} = -\alpha_{21} = \beta_1, \alpha_{34} = -\alpha_{43} = \beta_2, \ldots, \alpha_{2m-1, 2m} = -\alpha_{2m, 2m-1} = \beta_m,

all the other αij\alpha_{ij} being zero (cf. th. 1). Then the pfaffian of R=(αij)R = (\alpha_{ij}) is β1β2…βm\beta_1 \beta_2 \ldots \beta_m.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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