Proofs from THE BOOK
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The g-theorem proved by Billera, Lee, and Stanley states that a sequence is the g-vector of a simplicial polytope if and only if it is an M-sequence. For any d-dimensional simplicial polytope the face vector is gM"d where M"d is a certain matrix whose entries are sums of binomial coefficients. Bjorner found refined lower and upper bound theorems by showing that the (2x2)-minors of M"d are nonnegative. He conjectured that all minors of M"d are nonnegative and that is the result of this note.