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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
I have added in some additional comments plus some references. In particular there is a paper by Barbara Osofsky (The subscript of projective dimension, and the vanishing of _, Bull. Amer. Math. Soc. Volume 80, Number 1 (1974), 8-26.) which gives a neat discussion.
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