Multicomplexes and polynomials with real zeros

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. © 2006 Elsevier B.V. All rights reserved.

• Type: Journal
• Year: 2007
• Where: DM
• Authors: Jason Bell, Mark Skandera
• Keywords: DM 2007, Polynomials, Real Zeros, Simplicial Polytope