The g-theorem matrices are totally nonnegative |
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Authors: | Michael Björklund |
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Institution: | Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden |
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Abstract: | 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 gMd where Md is a certain matrix whose entries are sums of binomial coefficients. Björner found refined lower and upper bound theorems by showing that the (2×2)-minors of Md are nonnegative. He conjectured that all minors of Md are nonnegative and that is the result of this note. |
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Keywords: | Simplicial polytope g-theorem f-vector Totally nonnegative matrix |
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