Multicomplexes and polynomials with real zeros |
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Authors: | Jason Bell |
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Affiliation: | a Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC, Canada V5A 1S6 b Department of Mathematics, Lehigh University, Christmas-Saucon Hall, 14 East Packer Avenue, Bethlehem, PA 18015, USA |
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Abstract: | We show that each polynomial a(z)=1+a1z+?+adzd in N[z] having only real zeros is the f-polynomial of a multicomplex. It follows that a(z) is also the h-polynomial of a Cohen-Macaulay ring and is the g-polynomial of a simplicial polytope. We conjecture that a(z) is also the f-polynomial of a simplicial complex and show that the multicomplex result implies this in the special case that the zeros of a(z) belong to the real interval [-1,0). We also show that for fixed d the conjecture can fail for at most finitely many polynomials having the required form. |
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Keywords: | Simplicial complex Multicomplex Location of zeros of polynomials |
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