Multicomplexes and polynomials with real zeros

2Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

Abstract

We show that each polynomial a (z) = 1 + a1 z + ⋯ + ad zd 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.

Cite

CITATION STYLE

APA

Bell, J., & Skandera, M. (2007). Multicomplexes and polynomials with real zeros. Discrete Mathematics, 307(6), 668–682. https://doi.org/10.1016/j.disc.2006.07.020

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free