Bourbaki

Example 4

Tag 06EI, permanent. Cite it as [Bourbaki, Tag 06EI].

Algebra, chapter IV, § 6. Symmetric functions

By Example 3 of IV, p. 65, we have

M(3,0,0)=S(3,0,0)−3S(2,1,0)+3S(1,1,1) \mathbf{M}(3,0,0) = S(3,0,0) - 3S(2,1,0) + 3S(1,1,1)

for every integer n≥3n \geq 3, and so

M(3,0)=S(3,0)−3S(2,1) \mathbf{M}(3,0) = S(3,0) - 3S(2,1)

for n=2n = 2.

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

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Transcribed from the printed edition, 2003, Springer. Not translated.